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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

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.

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.