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Abstract: Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the “not later than” relationship. In this paper, we first introduce the novel notion of generalized comtraces, extensions of comtraces that can additionally model the “non-simultaneously” relationship. Then we study some basic algebraic properties and canonical representations of comtraces and generalized comtraces. Finally we analyze the relationship between generalized comtraces and generalized stratified order structures. The major technical contribution of this paper is a proof showing that generalized comtraces can be represented by generalized stratified order structures. [Copyright &y& Elsevier]

Abstract: “Clarithmetic” is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic instead of the more traditional classical or intuitionistic logics. Formulas of clarithmetical theories represent interactive computational problems, and their “truth” is understood as existence of an algorithmic solution. Imposing various complexity constraints on such solutions yields various versions of clarithmetic. The present paper introduces a system of clarithmetic for polynomial time computability, which is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be efficiently extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is written in a semitutorial style and targets readers with no prior familiarity with computability logic. [Copyright &y& Elsevier]

Abstract: We continue our study of the complexity of MSO-definable local temporal logics over concurrent systems that can be described by Mazurkiewicz traces. In previous papers, we showed that the satisfiability problem for any such logic is in PSPACE (provided the dependence alphabet is fixed, Gastin and Kuske (2003) ) and remains in PSPACE for all classical local temporal logics even if the dependence alphabet is part of the input, Gastin and Kuske (2007) . In this paper, we consider the uniform satisfiability problem for arbitrary MSO-definable local temporal logics. For this problem, we prove multi-exponential lower and upper bounds that depend on the number of alternations of set quantifiers present in the chosen MSO-modalities. [Copyright &y& Elsevier]

Abstract: The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism proposed by Ehrig and König and based on borrowed contexts (bcs), an instance of relative pushouts originally introduced by Milner and Leifer. The bc mechanism allows the effective construction of an lts that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of the lts distilled by exploiting the encoding of ccs processes: besides offering major technical contributions towards the simplification of the bc mechanism, a key result of our work is the proof that the bisimilarity on processes obtained via bcs coincides with the standard strong bisimilarity for ccs. [Copyright &y& Elsevier]

Abstract: This paper introduces (pronounce spades), a stochastic process algebra for discrete event systems, that extends traditional process algebra with timed actions whose delay is governed by general (a.o. continuous) probability distributions. The operational semantics is defined in terms of stochastic automata, a model that uses clocks—like in timed automata—to symbolically represent randomly timed systems, cf. the accompanying paper [P.R. D’Argenio, J.-P. Kateon, A theory of stochastic systems. Part I: Stochastic automata. Inf. Comput. (2005), to appear]. We show that stochastic automata and are equally expressive, and prove that the operational semantics of a term up to α-conversion of clocks, is unique (modulo symbolic bisimulation). (Open) probabilistic and structural bisimulation are proven to be congruences for, and are equipped with an equational theory. The equational theory is shown to be complete for structural bisimulation and allows to derive an expansion law. [Copyright &y& Elsevier]

Information integration systems provide uniform interfaces to varieties of heterogeneous information sources. For query answering in such systems, the current generation of query answering algorithms in local-as-view (source-centric) information integration systems all produce what has been thought of as “the best obtainable” answer, given the circumstances that the source-centric approach introduces incomplete information into the virtual global relations. However, this “best obtainable” answer does not include all information that can be extracted from the sources because it does not allow partial information. Neither does the “best obtainable” answer allow for composition of queries, meaning that querying a result of a previous query will not be equivalentto the composition of the two queries. In this paper, we provide a foundation for information integration, based on the algebraic theory of incomplete information. Our framework allows us to define the semantics of partial facts and introduce the notion of the exact answer—that is the answer that includes partial facts. We show that querying under the exact answer semantics is compositional. We also present two methods for actually computing the exact answer. The first method is tableau-based, and it is a generalization of the “inverse-rules” approach. The second, much more efficient method, is a generalization of the rewriting approach, and it is based on partial containment mappings introduced in the paper. [Copyright &y& Elsevier]

This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based. [Copyright &y& Elsevier]

This paper introduces a novel (bi)simulation-based faster-than preorder which relates asynchronous processes, where the relative speeds of system components are indeterminate, with respect to their worst-case timing behavior. The study is conducted for a conservative extension of the process algebra CCS, called TACS, which permits the specification of upper time bounds on action occurrences. TACS complements work in plain process algebras which compares asynchronous processes with respect to their functional reactive behavior only, and in timed process algebras which focus on analyzing synchronous processes. The most unusual contribution is in showing that the proposed faster-than preorder coincides with several other preorders, two of which consider the absolute times at which actions occur in system runs. The paper also develops the semantic theory of TACS by studying congruence properties, equational laws, and abstractions from internal actions. Two examples, one dealing with mail delivery and one relating two implementations of a simple storage system, testify to the practical utility of the new theory. [Copyright &y& Elsevier]

Abstract: Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. Recently the language has been extended by introducing user-definable (static or dynamic) rule priorities. The resulting language allows a better control over execution while retaining a declarative and flexible style of programming. In this paper we study the expressive power of this language. We first show that, in the presence of priorities, differently from the case of standard CHR, considering more than two atoms in the heads of rules does not augment the expressive power of the language. Next we show that also dynamic priorities do not augment the expressive power w.r.t. static priorities. These results are proved by providing explicitly a translation of one language into another one, which preserves a reference semantics. Finally we show that CHR with priorities is strictly more expressive than standard CHR (under the theoretical operational semantics). This result is obtained by adapting to the CHR case a notion of language encoding which allows to compare Turing powerful languages. [Copyright &y& Elsevier]

Abstract: We consider the problem of computing a maximum cardinality popular matching in a bipartite graph where each vertex ranks its neighbors in a strict order of preference. Such a graph is called an instance of the stable marriage problem with strict preferences and incomplete lists. A matching is popular if for every matching M in G, the number of vertices that prefer M to is at most the number of vertices that prefer to M. Every stable matching of G is popular, however a stable matching is a minimum cardinality popular matching. The complexity of computing a maximum cardinality popular matching was unknown. In this paper we show a simple characterization of popular matchings in . We also show a sufficient condition for a popular matching to be a maximum cardinality popular matching. We construct a matching that satisfies our characterization and sufficient condition in time, where and . Thus the maximum cardinality popular matching problem in can be solved in time. [Copyright &y& Elsevier]

Abstract: We consider the conditional covering problem in an undirected network, in which each vertex represents a demand point that must be covered by a facility as well as a potential facility site. Each facility can cover all vertices within a given coverage radius, except the vertex at which the facility is located. The objective is to locate facilities to cover all vertices such that the total facility location cost is minimized. In this paper, new upper bounds are proposed for the conditional covering problem on paths, cycles, extended stars, and trees. In particular, we provide an -time algorithm for paths, an -time algorithm for cycles, an -time algorithm for extended stars, and an -time algorithm for trees. Our algorithms for paths, extended stars, and trees improve the previous upper bounds from , , and , respectively. [Copyright &y& Elsevier]

Abstract: In the graph searching game the opponents are a set of searchers and a fugitive in a graph. The searchers try to capture the fugitive by applying some sequence of moves that include placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture by moving along unguarded paths. The search number of a graph is the minimum number of searchers required to guarantee the capture of the fugitive. In this paper, we initiate the study of this game under the natural restriction of connectivity where we demand that in each step of the search the locations of the graph that are clean (i.e. non-accessible to the fugitive) remain connected. We give evidence that many of the standard mathematical tools used so far in classic graph searching fail under the connectivity requirement. We also settle the question on “the price of connectivity”, that is, how many searchers more are required for searching a graph when the connectivity demand is imposed. We make estimations of the price of connectivity on general graphs and we provide tight bounds for the case of trees. In particular, for an n-vertex graph the ratio between the connected searching number and the non-connected one is while for trees this ratio is always at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for all graphs. Our combinatorial results imply a complete characterization of connected graph searching on trees. It is based on a forbidden-graph characterization of the connected search number. We prove that the connected search game is monotone for trees, i.e. restricting search strategies to only those where the clean territories increase monotonically does not require more searchers. A consequence of our results is that the connected search number can be computed in polynomial time on trees, moreover, we show how to make this algorithm distributed. Finally, we reveal connections of this parameter to other invariants on trees such as the Horton–Strahler number. [Copyright &y& Elsevier]

Abstract: This paper proposes an approach for extending to graphs the close relation between proofs and innocent strategies. We work in the setting of L-nets, introduced by Faggian and Maurel as a game model of concurrent interaction. We show how L-nets satisfying an additional condition, which we call LS-nets, can be sequentialized into traditional tree-like strategies. Conversely, sequential strategies can be relaxed into more asynchronous ones. We develop an algebra of constructors and destructors that serve to build and decompose graph strategies, and to describe a class of minimally sequential graph strategies, which can be seen as an abstract kind of multiplicative–additive proof nets. [Copyright &y& Elsevier]

Abstract: Goldʼs original paper on inductive inference introduced a notion of an optimal learner. Intuitively, a learner identifies a class of objects optimally iff there is no other learner that: requires as little of each presentation of each object in the class in order to identify that object, and, for some presentation of some object in the class, requires less of that presentation in order to identify that object. Beick considered this notion in the context of function learning, and gave an intuitive characterization of an optimal function learner. Jantke and Beick subsequently characterized the classes of functions that are algorithmically, optimally identifiable. Herein, Goldʼs notion is considered in the context of language learning. It is shown that a characterization of optimal language learners analogous to Beickʼs does not hold. It is also shown that the classes of languages that are algorithmically, optimally identifiable cannot be characterized in a manner analogous to that of Jantke and Beick. Other interesting results concerning optimal language learning include the following. It is shown that strong non-U-shapedness, a property involved in Beickʼs characterization of optimal function learners, does not restrict algorithmic language learning power. It is also shown that, for an arbitrary optimal learner F of a class of languages , F optimally identifies a subclass of iff F is class-preserving with respect to . [Copyright &y& Elsevier]

Abstract: In this paper, we introduce model-checking games that allow local second-order power on sets of independent transitions in the underlying partial order models where the games are played. Since the interleaving semantics of such models is not considered, some problems that may arise when using interleaving representations are avoided and new decidability results for partial order models of concurrency are achieved. The games are shown to be sound and complete, and therefore determined. While in the interleaving case they coincide with the local model-checking games for the -calculus, in a partial order setting they verify properties of a number of fixpoint modal logics that can specify, in concurrent systems with partial order semantics, several properties not expressible with the -calculus. The games underpin a novel decision procedure for model-checking all temporal properties of a class of infinite and regular event structures, thus improving, in terms of temporal expressive power, previous results in the literature. [Copyright &y& Elsevier]

Abstract: We consider two-player parity games with imperfect information in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e., to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recently, an algorithm that avoids the inefficient subset construction has been proposed. The algorithm performs a fixed-point computation in a lattice of antichains, thus maintaining a succinct representation of state sets. However, this representation does not allow to recover winning strategies. In this paper, we build on the antichain approach to develop an algorithm for constructing the winning strategies in parity games of imperfect information. One major obstacle in adapting the classical procedure is that the complementation of attractor sets would break the invariant of downward-closedness on which the antichain representation relies. We overcome this difficulty by decomposing problem instances recursively into games with a combination of reachability, safety, and simpler parity conditions. We also report on an experimental implementation of our algorithm; to our knowledge, this is the first implementation of a procedure for solving imperfect-information parity games on graphs. [ABSTRACT FROM AUTHOR]

Abstract: Termination is one of the most interesting problems when dealing with context-sensitive rewrite systems. Although a good number of techniques for proving termination of context-sensitive rewriting (CSR) have been proposed so far, the adaptation to CSR of the dependency pair approach, one of the most powerful techniques for proving termination of rewriting, took some time and was possible only after introducing some new notions like collapsing dependency pairs, which are specific for CSR. In this paper, we develop the notion of context-sensitive dependency pair (CSDP) and show how to use CSDPs in proofs of termination of CSR. The implementation and practical use of the developed techniques yield a novel and powerful framework which improves the current state-of-the-art of methods for automatically proving termination of CSR. [Copyright &y& Elsevier]

Abstract: We address the problem of finding nice labellings for event structures of degree 3. We develop a minimum theory by which we prove that the index of an event structure of degree 3 is bounded by a linear function of the height. The main theorem of the paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors. We exemplify how to use this theorem to construct upper bounds for the index of other event structures of degree 3. [Copyright &y& Elsevier]

Abstract: It is well known that bisimulation on -expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features beyond pure equational Horn logic: either rules that are impure by involving non-equational side-conditions, or rules that are schematically infinitary like the congruence rule which is not Horn. It is an open question whether these complications cannot be avoided in the proof-theoretically and computationally clean and powerful setting of second-order equational Horn logic. This paper presents a positive and a negative result regarding the axiomatisability of observational congruence in equational Horn logic. Firstly, we show how Milner’s impure rule system can be reworked into a pure Horn axiomatisation that is complete for guarded processes. Secondly, we prove that for unguarded processes, both Milner’s unique fixed point rule and Bloom/Ésik’s GA rule are incomplete without the congruence rule, and neither system has a complete extension in rank-1 equational axioms. It remains open whether there are higher-rank equational axioms or other Horn rules which would render Milner’s or Bloom/Ésik’s axiomatisations complete. [Copyright &y& Elsevier]

Abstract: For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions. Each of the heuristics produces tree decompositions whose width may be larger than the optimal width. However, experiments show that in many cases, the heuristics give tree decompositions whose width is close to the exact treewidth of the input graphs. [Copyright &y& Elsevier]

Abstract: We investigate weak bisimulation of probabilistic systems in the presence of nondeterminism, i.e. labelled concurrent Markov chains (LCMC) with silent transitions. We develop an approach based on allowing convex combinations of computations, similar to Segala and Lynch’s use of randomized schedulers. The definition of weak bisimulation destroys the additivity property of the probability distributions, yielding instead capacities. The mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with bounds on the possible probabilities rather than with their exact values. Our analysis leads to three new developments: [•] We identify a characterization of “image finiteness” for countable-state systems and present a new definition of weak bisimulation for these LCMCs. We prove that our definition coincides with that of Philippou, Lee and Sokolsky for finite state systems. [•] We show that bisimilar states have matching computations. The notion of matching involves convex combinations of transitions. [•] We study a minor variant of the probabilistic logic – the variation arises from an extra path formula to address action labels. We show that bisimulation is sound and complete for this variant of . This is an extended complete version of a paper that was presented at CONCUR 2002. [Copyright &y& Elsevier]

Abstract: The use of automata techniques to prove the termination of string rewrite systems and left-linear term rewrite systems is advocated by Geser et al. in a recent sequence of papers. We extend their work to non-left-linear rewrite systems. The key to this extension is the introduction of so-called raise rules and the use of tree automata that are not quite deterministic. Furthermore, to increase the applicability of the method we show how it can be incorporated into the dependency pair framework. To achieve this we introduce two new enrichments which take the special properties of dependency pair problems into account. [Copyright &y& Elsevier]

Abstract: This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We give a complete list of FA-presentable one-relation semigroups and compare the classes of FA-presentable semigroups and automatic semigroups. [Copyright &y& Elsevier]

Abstract: In this paper we study the link between formal and cryptographic models for security protocols in the presence of passive adversaries. In contrast to other works, we do not consider a fixed set of primitives but aim at results for arbitrary equational theories. We define a framework for comparing a cryptographic implementation and its idealization with respect to various security notions. In particular, we concentrate on the computational soundness of static equivalence, a standard tool in cryptographic pi calculi. We present a soundness criterion, which for many theories is not only sufficient but also necessary. Finally, to illustrate our framework, we establish the soundness of static equivalence for the exclusive OR and a theory of ciphers and lists. [Copyright &y& Elsevier]

Abstract: Logical relations are a fundamental and powerful tool for reasoning about programs in languages with parametric polymorphism. Logical relations suitable for reasoning about observational behavior in polymorphic calculi supporting various programming language features have been introduced in recent years. Unfortunately, the calculi studied are typically idealized, and the results obtained for them offer only partial insight into the impact of such features on observational behavior in implemented languages. In this paper we show how to bring reasoning via logical relations closer to bear on real languages by deriving results that are more pertinent to an intermediate language for the (mostly) lazy functional language Haskell like GHC Core. To provide a more fine-grained analysis of program behavior than is possible by reasoning about program equivalence alone, we work with an abstract notion of relating observational behavior of computations which has among its specializations both observational equivalence and observational approximation. We take selective strictness into account, and we consider the impact of different kinds of computational failure, e.g., divergence versus failed pattern matching, because such distinctions are significant in practice. Once distinguished, the relative definedness of different failure causes needs to be considered, because different orders here induce different observational relations on programs (including the choice between equivalence and approximation). Our main contribution is the construction of an entire family of logical relations, parameterized over a definedness order on failure causes, each member of which characterizes the corresponding observational relation. Although we deal with properties very much tied to types, we base our results on a type-erasing semantics since this is more faithful to actual implementations. [Copyright &y& Elsevier]

Abstract: Dπ is a simple distributed extension of the π-calculus in which agents are explicitly located, and may use an explicit migration construct to move between locations. In this paper, we introduce passports to control those migrations; in order to gain access to a location agents are now expected to show some credentials, granted by the destination location. Passports are tied to specific locations, from which migration is permitted. We describe a type system for these passports, which includes a novel use of dependent types, and prove that well-typing enforces the desired behaviour in migrating processes. Passports allow locations to control incoming processes. This induces major modifications to the observations which can be made of agent-based systems. Using the type system we describe these observations, and use them to build a loyal notion of observational equivalence for this setting. Finally we provide a complete proof technique in the form of a bisimilarity for establishing equivalences between systems. [Copyright &y& Elsevier]

Abstract: Van Glabbeek presented the linear time–branching time spectrum of behavioral semantics. He studied these semantics in the setting of the basic process algebra BCCSP, and gave finite, sound and ground-complete, axiomatizations for most of these semantics. Groote proved for some of van Glabbeek’s axiomatizations that they are -complete, meaning that an equation can be derived if (and only if) all of its closed instantiations can be derived. In this paper, we settle the remaining open questions for all the semantics in the linear time–branching time spectrum, either positively by giving a finite sound and ground-complete axiomatization that is -complete, or negatively by proving that such a finite basis for the equational theory does not exist. We prove that in case of a finite alphabet with at least two actions, failure semantics affords a finite basis, while for ready simulation, completed simulation, simulation, possible worlds, ready trace, failure trace and ready semantics, such a finite basis does not exist. Completed simulation semantics also lacks a finite basis in case of an infinite alphabet of actions. [Copyright &y& Elsevier]

Abstract: This paper compares the expressiveness of different fragments of ambient calculi via leader election problems. We consider Mobile Ambients (MA), Safe Ambients (SA) and the Push and Pull Ambient Calculus (PAC). Cardelli and Gordon encoded the asynchronous π-calculus into MA. Zimmer has shown that the synchronous π-calculus without choice can be encoded in pure (no communication) SA. We show that pure MA without restriction has symmetric electoral systems, that is, it is possible to solve the problem of electing a leader in a symmetric network. By the work of Palamidessi, this implies that this fragment of MA is not encodable (under certain conditions) in the π-calculus with separate choice. Moreover, we use the same technique to show that fragments of SA and PAC are not encodable (under certain conditions) in the π-calculus with separate choice. We also show that particular fragments of ambient calculi do not admit a solution to leader election problems, in the same way as the π-calculus with separate choice. This yields a fine-grained hierarchy within ambient calculi. [Copyright &y& Elsevier]

Abstract: In this paper, we present , a fully typed λ-calculus based on the intersection-type system discipline, which is a counterpart àla Church of the type assignment system as invented by Coppo and Dezani. The relationship between and the intersection type assignment system is the standard isomorphism between typed and type assignment system, and so the typed language inherits from the untyped system all the good properties, like subject reduction and strong normalization. Moreover, both type checking and type reconstruction are decidable. [Copyright &y& Elsevier]

Abstract: This paper investigates the word problem for inverse monoids generated by a set Γ subject to relations of the form e = f, where e and f are both idempotents in the free inverse monoid generated by Γ. It is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a RAM as well as in deterministic logarithmic space, which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presentation is part of the input, EXPTIME-completeness is shown. For the Cayley-graphs of these monoids, it is shown that the first-order theory with regular path predicates is decidable. Regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language. As a corollary, the decidability of the generalized word problem is deduced. [Copyright &y& Elsevier]

Abstract: Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper, we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of (semi-weighted) graph grammars and the category of prime algebraic domains, which factorises through the category of occurrence grammars and the category of asymmetric event structures. For general, possibly nonsemi-weighted single-pushout grammars, we define an analogous functorial concurrent semantics, which, however, is not characterised as an adjunction. Similar results can be obtained for double-pushout graph grammars, under the assumptions that nodes are never deleted. [Copyright &y& Elsevier]

Abstract: Visual cryptography schemes have been introduced in 1994 by Naor and Shamir. Their idea was to encode a secret image into n shadow images and to give exactly one such shadow image to each member of a group P of n persons. Whereas most work in recent years has been done concerning the problem of qualified and forbidden subsets of P or the question of contrast optimizing, in this paper we study extended visual cryptography schemes, i.e., shared secret systems where any subset of P shares its own secret. [Copyright &y& Elsevier]

Abstract: The Counting Constraint Satisfaction Problem (#CSP) can be expressed as follows: given a set of variables, a set of values that can be taken by the variables, and a set of constraints specifying some restrictions on the values that can be taken simultaneously by some variables, determine the number of assignments of values to variables that satisfy all the constraints. The #CSP provides a general framework for numerous counting combinatorial problems including counting satisfying assignments to a propositional formula, counting graph homomorphisms, graph reliability and many others. This problem can be parametrized by the set of relations that may appear in a constraint. In this paper we start a systematic study of subclasses of the #CSP restricted in this way. The ultimate goal of this investigation is to distinguish those restricted subclasses of the #CSP which are solvable in polynomial time from those which are not. We show that the complexity of any restricted #CSP class on a finite domain can be deduced from the properties of polymorphisms of the allowed constraints, similar to that for the decision constraint satisfaction problem. Then we prove that if a subclass of the #CSP is solvable in polynomial time, then constraints allowed by the class satisfy some very restrictive condition: they need to have a Mal’tsev polymorphism, that is a ternary operation such that . This condition uniformly explains many existing complexity results for particular cases of the #CSP, including the dichotomy results for the problem of counting graph homomorphisms, and it allows us to obtain new results. [Copyright &y& Elsevier]

Abstract: Cryptographic protocols are small programs which involve a high level of concurrency and which are difficult to analyze by hand. The most successful methods to verify such protocols are based on rewriting techniques and automated deduction in order to implement or mimic the process calculus describing the execution of a protocol. We are interested in the intruder deduction problem, that is vulnerability to passive attacks in presence of equational theories which model the protocol specification and properties of the cryptographic operators. In the present paper, we consider the case where the encryption distributes over the operator of an Abelian group or over an exclusive-or operator. We prove decidability of the intruder deduction problem in both cases. We obtain a PTIME decision procedure in a restricted case, the so-called binary case. These decision procedures are based on a careful analysis of the proof system modeling the deductive power of the intruder, taking into account the algebraic properties of the equational theories under consideration. The analysis of the deduction rules interacting with the equational theory relies on the manipulation of -modules in the general case, and on results from prefix rewriting in the binary case. [Copyright &y& Elsevier]

Abstract: In this paper we present a solution to the long-standing problem of characterising the coarsest liveness-preserving pre-congruence with respect to a full (TCSP-inspired) process algebra. In fact, we present two distinct characterisations, which give rise to the same relation: an operational one based on a De Nicola–Hennessy-like testing modality which we call should-testing, and a denotational one based on a refined notion of failures. One of the distinguishing characteristics of the should-testing pre-congruence is that it abstracts from divergences in the same way as Milner’s observation congruence, and as a consequence is strictly coarser than observation congruence. In other words, should-testing has a built-in fairness assumption. This is in itself a property long sought-after; it is in notable contrast to the well-known must-testing of De Nicola and Hennessy (denotationally characterised by a combination of failures and divergences), which treats divergence as catastrophic and hence is incompatible with observation congruence. Due to these characteristics, should-testing supports modular reasoning and allows to use the proof techniques of observation congruence, but also supports additional laws and techniques. Moreover, we show decidability of should-testing (on the basis of the denotational characterisation). Finally, we demonstrate its advantages by the application to a number of examples, including a scheduling problem, a version of the Alternating Bit-protocol, and fair lossy communication channels. [Copyright &y& Elsevier]

Abstract: Term algebras can model recursive data structures which are widely used in programming languages. To verify programs we must be able to reason about these structures. However, as programming languages often involve multiple data domains, in program verification decision procedures for a single theory are usually not applicable. An important class of mixed constraints consists of combinations of data structures with integer constraints on the size of data structures. Such constraints can express memory safety properties such as absence of memory overflow and out-of-bound array access, which are crucial for program correctness. In this paper we extend the theory of term algebras with the length function which maps a term to its size, resulting in a combined theory of term algebras and Presburger arithmetic. This arithmetic extension provides a natural but tight coupling between the two theories, and hence the general purpose combination methods like Nelson-Oppen combination are not applicable. We present decision procedures for quantifier-free theories in structures with an infinite constant domain and with a finite constant domain. We also present a quantifier elimination procedure for the extended first-order theory that can remove a block of existential quantifiers in one step. [Copyright &y& Elsevier]

Abstract: The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure—only involving clauses over the alphabet of either one, but not both, of the theories—when refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally, we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories. [Copyright &y& Elsevier]

Abstract: Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics—which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics. [Copyright &y& Elsevier]

Abstract: When a process is capable of executing an unbounded number of non-observable actions it is said to be divergent. Different capabilities of an observer to identify this phenomena along the execution leads to different divergent sensitive semantics. This paper develops sound and complete axiomatisations for the divergence sensitive spectrum of weak bisimulation equivalence. The axiomatisations separates the axioms concerning recursion and those that capture the essence of diverging behaviour. [Copyright &y& Elsevier]

Abstract: Model checking is a formal technique for proving the correctness of a system with respect to a desired behavior. This is accomplished by checking whether a structure representing the system (typically a labeled transition system) satisfies a temporal logic formula describing the expected behavior. Model checking has a number of advantages over traditional approaches that are based on simulation and testing: it is completely automatic and when the verification fails it returns a counterexample that can be used to pinpoint the source of the error. Nevertheless, model checking techniques often fail because of the state explosion problem: transition systems grow exponentially with the number of components. The aim of this paper is to attack the state explosion problem that may arise when looking for deadlocks in concurrent systems described through the calculus of communicating systems. We propose to use heuristics-based techniques, namely the A* algorithm, both to guide the search without constructing the complete transition system, and to provide minimal counterexamples. We have realized a prototype tool to evaluate the methodology. Experiments we have conducted on processes of different size show the benefit from using our technique against building the whole state space, or applying some other methods. [Copyright &y& Elsevier]

Abstract: The Seal Calculus is a process language for describing mobile computation. Threads and resources are tree structured; the nodes thereof correspond to agents, the units of mobility. The Calculus extends a π-calculus core with synchronous, objective mobility of agents over channels. This paper systematically compares all previous variants of Seal Calculus. We study their operational behaviour with labelled transition systems and bisimulations; by comparing the resulting algebraic theories we highlight the differences between these apparently similar approaches. This leads us to identify the dialect of Seal that is most amenable to operational reasoning and can form the basis of a distributed programming language. We propose type systems for characterising the communications in which an agent can engage. The type systems thus enforce a discipline of agent mobility, since the latter is coded in terms of higher-order communication. [Copyright &y& Elsevier]

Abstract: The paper considers the problem of checking abstraction between two finite-state fair discrete systems. In automata-theoretic terms this is trace inclusion between two nondeterministic Streett automata. We propose to reduce this problem to an algorithm for checking fair simulation between two generalized Büchi automata. For solving this question we present a new triply nested μ-calculus formula which can be implemented by symbolic methods. We then show that every trace inclusion of this type can be solved by fair simulation, provided we augment the concrete system (the contained automaton) by an appropriate ‘non-constraining’ automaton. This establishes that fair simulation offers a complete method for checking trace inclusion for finite-state systems. We illustrate the feasibility of the approach by algorithmically checking abstraction between finite state systems whose abstraction could only be verified by deductive methods up to now. [Copyright &y& Elsevier]

Abstract: First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. Although a complete and correct resolution-style calculus has already been suggested for this specific fragment, this calculus involves constructions too complex to be of practical value. In this paper, we develop a machine-oriented clausal resolution method which features radically simplified proof search. We first define a normal form for monodic formulae and then introduce a novel resolution calculus that can be applied to formulae in this normal form. By careful encoding, parts of the calculus can be implemented using classical first-order resolution and can, thus, be efficiently implemented. We prove correctness and completeness results for the calculus and illustrate it on a comprehensive example. An implementation of the method is briefly discussed. [Copyright &y& Elsevier]

Record concatenation, multiple inheritance, and multiple-object cloning are closely related and part of various language designs. For example, in Cardelli’s untyped Obliq language, a new object can be constructed from several existing objects by cloning followed by concatenation; an error is given in case of field name conflicts. Type systems for record concatenation have been studied by Wand, Harper and Pierce, Remy, and others; and type inference for the combination of record concatenation and subtyping has been studied by Sulzmann and by Pottier. In this paper we present a type inference algorithm for record concatenation, subtyping, and recursive types. Our example language is the Abadi–Cardelli object calculus extended with a concatenation operator. Our algorithm enables type checking of Obliq programs without changing the programs at all. We prove that the type inference problem is NP-complete. [Copyright &y& Elsevier]

In this paper we consider four possible definitions for extending a partially defined Boolean function in which the input contains some missing bits. We show somewhat surprisingly that, for many general and frequently used families of function classes, three of these notions of an extension are mathematically equivalent, though such an equivalence does not hold universally, as demonstrated by several examples. [Copyright &y& Elsevier]