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Many practical applications require synthesizing directed graphs that satisfy the acyclic constraint along with some side constraints. Several methods have been devised for encoding acyclicity of directed graphs into SAT, each of which is based on a cycle-detecting algorithm. The leaf-elimination encoding (LEE) repeatedly eliminates leaves from the graph, and judges the graph to be acyclic if the graph becomes empty at a certain time. The vertex-elimination encoding (VEE) exploits the property that the cyclicity of the resulting graph produced by the vertex-elimination operation entails the cyclicity of the original graph. While VEE is significantly smaller than the transitive-closure encoding for sparse graphs, it generates prohibitively large encodings for large dense graphs. This paper reports on a comparison study of four SAT encodings for acyclicity of directed graphs, namely, LEE using unary encoding for time variables (LEE-u), LEE using binary encoding for time variables (LEE-b), VEE, and a hybrid encoding which combines LEE-b and VEE. The results show that the hybrid encoding significantly outperforms the others.

ICLP is the premier international event for presenting research in logic programming. Contributions to ICLP 2021 were sought in all areas of logic programming, including but not limited to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages issues: Concurrency, Objects, Coordination, Mobility, Higher order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming techniques. Programming support: Program analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualization. Implementation: Compilation, Virtual machines, Memory management, Parallel and Distributed execution, Constraint handling rules, Tabling, Foreign interfaces, User interfaces. Related Paradigms and Synergies: Inductive and coinductive logic programming, Constraint logic programming, Answer set programming, Interaction with SAT, SMT and CSP solvers, Theorem proving, Argumentation, Probabilistic programming, Machine learning. Applications: Databases, Big data, Data integration and federation, Software engineering, Natural language processing, Web and semantic web, Agents, Artificial intelligence, Computational life sciences, Cyber-security, Robotics, Education.

Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The programs demonstrate the modeling capabilities of the Picat language and the solving efficiency of the cutting-edge SAT solvers empowered with effective encodings., Comment: In Proceedings ICLP 2021, arXiv:2109.07914

The at-most-k constraint is ubiquitous in combinatorial problems, and numerous SAT encodings are available for the constraint. Prior experiments have shown the competitiveness of the sequential-counter encoding for k $>$ 1, and have excluded the parallel-counter encoding, which is more compact that the binary-adder encoding, from consideration due to its incapability of enforcing arc consistency through unit propagation. This paper presents an experiment that shows astounding performance of the binary-adder encoding for the at-most-k constraint.

The multi-agent pathfinding (MAPF) problem has attracted considerable attention because of its relation to practical applications. The majority of solutions for MAPF are algorithmic. Recently, declarative solutions that reduce MAPF to encodings for off-the-shelf solvers have achieved remarkable success. We present a constraint-based declarative model for MAPF, together with its implementation in Picat, which uses SAT and MIP. We consider both the makespan and the sum-of-costs objectives, and propose a preprocessing technique for improving the performance of the model. Experimental results show that the implementation using SAT is highly competitive. We also analyze the high performance of the SAT solution by relating it to the SAT encoding algorithms that are used in the Picat compiler.

This paper describes Picat's planner, its implementation, and planning models for several domains used in International Planning Competition (IPC) 2014. Picat's planner is implemented by use of tabling. During search, every state encountered is tabled, and tabled states are used to effectively perform resource-bounded search. In Picat, structured data can be used to avoid enumerating all possible permutations of objects, and term sharing is used to avoid duplication of common state data. This paper presents several modeling techniques through the example models, ranging from designing state representations to facilitate data sharing and symmetry breaking, encoding actions with operations for efficient precondition checking and state updating, to incorporating domain knowledge and heuristics. Broadly, this paper demonstrates the effectiveness of tabled logic programming for planning, and argues the importance of modeling despite recent significant progress in domain-independent PDDL planners., Comment: 27 pages in TPLP 2015

Tabling has been used for some time to improve efficiency of Prolog programs by memorizing answered queries. The same idea can be naturally used to memorize visited states during search for planning. In this paper we present a planner developed in the Picat language to solve the Petrobras planning problem. Picat is a novel Prolog-like language that provides pattern matching, deterministic and non-deterministic rules, and tabling as its core modelling and solving features. We demonstrate these capabilities using the Petrobras problem, where the goal is to plan transport of cargo items from ports to platforms using vessels with limited capacity. Monte Carlo Tree Search has been so far the best technique to tackle this problem and we will show that by using tabling we can achieve much better runtime efficiency and better plan quality., Comment: To appear in Theory and Practice of Logic Programming (TPLP)

Picat, a new member of the logic programming family, follows a different doctrine than Prolog in offering the core logic programming concepts: arrays and maps as built-in data types; implicit pattern matching with explicit unification and explicit non-determinism; functions for deterministic computations; and loops for convenient scripting and modeling purposes. Picat provides facilities for solving combinatorial search problems, including a common interface with CP, SAT, and MIP solvers, tabling for dynamic programming, and a module for planning. Picat's planner module, which is implemented by the use of tabling, has produced surprising and encouraging results. Thanks to term-sharing and resource-bounded tabled search, Picat overwhelmingly outperforms the cutting-edge ASP and PDDL planners on the planning benchmarks used in recent ASP competitions.

This talk will give the design principles of the Picat language (http://www.picat-lang.org), highlight the high-level and intuitive abstractions provided by Picat for easy programming, and contemplate why Picat is more robust and scalable than Prolog and could be more accessible than Prolog to ordinary programmers for scripting and modeling tasks.

This talk will give the design principles of the Picat language (http://www.picat-lang.org), highlight the high-level and intuitive abstractions provided by Picat for easy programming, and contemplate why Picat is more robust and scalable than Prolog and could be more accessible than Prolog to ordinary programmers for scripting and modeling tasks.

The Frame-Stewart algorithm for the 4-peg variant of the Tower of Hanoi, introduced in 1941, partitions disks into intermediate towers before moving the remaining disks to their destination. Algorithms that partition the disks have not been proven to be optimal, although they have been verified for up to 30 disks. This paper presents a dynamic programming approach to this algorithm, using tabling in B-Prolog. This study uses a variation of the problem, involving configurations of disks, in order to contrast the tabling approach with the approaches utilized by other solvers. A comparison of different partitioning locations for the Frame-Stewart algorithm indicates that, although certain partitions are optimal for the classic problem, they need to be modified for certain configurations, and that random configurations might require an entirely new algorithm., Comment: Appeared in CICLOPS 2012. 15 Pages, 2 Figures

Current tabling systems suffer from an increase in space complexity, time complexity or both when dealing with sequences due to the use of data structures for tabled subgoals and answers and the need to copy terms into and from the table area. This symptom can be seen in not only B-Prolog, which uses hash tables, but also systems that use tries such as XSB and YAP. In this paper, we apply hash-consing to tabling structured data in B-Prolog. While hash-consing can reduce the space consumption when sharing is effective, it does not change the time complexity. We enhance hash-consing with two techniques, called input sharing and hash code memoization, for reducing the time complexity by avoiding computing hash codes for certain terms. The improved system is able to eliminate the extra linear factor in the old system for processing sequences, thus significantly enhancing the scalability of applications such as language parsing and bio-sequence analysis applications. We confirm this improvement with experimental results., Comment: 16 pages; TPLP, 2012

B-Prolog is a high-performance implementation of the standard Prolog language with several extensions including matching clauses, action rules for event handling, finite-domain constraint solving, arrays and hash tables, declarative loop constructs, and tabling. The B-Prolog system is based on the TOAM architecture which differs from the WAM mainly in that (1) arguments are passed old-fashionedly through the stack, (2) only one frame is used for each predicate call, and (3) instructions are provided for encoding matching trees. The most recent architecture, called TOAM Jr., departs further from the WAM in that it employs no registers for arguments or temporary variables, and provides variable-size instructions for encoding predicate calls. This paper gives an overview of the language features and a detailed description of the TOAM Jr. architecture, including architectural support for action rules and tabling., Comment: 30 pages

Online proceedings of the Joint Workshop on Implementation of Constraint Logic Programming Systems and Logic-based Methods in Programming Environments (CICLOPS-WLPE 2010), Edinburgh, Scotland, U.K., July 15, 2010.

Recently, the iterative approach named linear tabling has received considerable attention because of its simplicity, ease of implementation, and good space efficiency. Linear tabling is a framework from which different methods can be derived based on the strategies used in handling looping subgoals. One decision concerns when answers are consumed and returned. This paper describes two strategies, namely, {\it lazy} and {\it eager} strategies, and compares them both qualitatively and quantitatively. The results indicate that, while the lazy strategy has good locality and is well suited for finding all solutions, the eager strategy is comparable in speed with the lazy strategy and is well suited for programs with cuts. Linear tabling relies on depth-first iterative deepening rather than suspension to compute fixpoints. Each cluster of inter-dependent subgoals as represented by a top-most looping subgoal is iteratively evaluated until no subgoal in it can produce any new answers. Naive re-evaluation of all looping subgoals, albeit simple, may be computationally unacceptable. In this paper, we also introduce semi-naive optimization, an effective technique employed in bottom-up evaluation of logic programs to avoid redundant joins of answers, into linear tabling. We give the conditions for the technique to be safe (i.e. sound and complete) and propose an optimization technique called {\it early answer promotion} to enhance its effectiveness. Benchmarking in B-Prolog demonstrates that with this optimization linear tabling compares favorably well in speed with the state-of-the-art implementation of SLG., Comment: 29 pages, 1 figure, TPLP

In this paper, we propose a new language, called AR ({\it Action Rules}), and describe how various propagators for finite-domain constraints can be implemented in it. An action rule specifies a pattern for agents, an action that the agents can carry out, and an event pattern for events that can activate the agents. AR combines the goal-oriented execution model of logic programming with the event-driven execution model. This hybrid execution model facilitates programming constraint propagators. A propagator for a constraint is an agent that maintains the consistency of the constraint and is activated by the updates of the domain variables in the constraint. AR has a much stronger descriptive power than {\it indexicals}, the language widely used in the current finite-domain constraint systems, and is flexible for implementing not only interval-consistency but also arc-consistency algorithms. As examples, we present a weak arc-consistency propagator for the {\tt all\_distinct} constraint and a hybrid algorithm for n-ary linear equality constraints. B-Prolog has been extended to accommodate action rules. Benchmarking shows that B-Prolog as a CLP(FD) system significantly outperforms other CLP(FD) systems.

Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG- resolution, and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM., Comment: To appear as the first accepted paper in Theory and Practice of Logic Programming (http://www.cwi.nl/projects/alp/TPLP)