A Parallel semantics for normal logic programs plus time

It is proposed that Normal Logic Programs with an explicit time ordering are a suitable basis for a general purpose parallel programming language. Examples show that such a language can accept real-time external inputs and outputs, and mimic assignment, all without departing from its pure logical semantics. This paper describes a fully incremental bottom-up interpreter that supports a wide range of parallel execution strategies and can extract significant potential parallelism from programs with complex dependencies

Graph Based Reduction of Program Verification Conditions

Increasing the automaticity of proofs in deductive verification of C programs is a challenging task. When applied to industrial C programs known heuristics to generate simpler verification conditions are not efficient enough. This is mainly due to their size and a high number of irrelevant hypotheses. This work presents a strategy to reduce program verification conditions by selecting their relevant hypotheses. The relevance of a hypothesis is determined by the combination of a syntactic analysis and two graph traversals. The first graph is labeled by constants and the second one by the predicates in the axioms. The approach is applied on a benchmark arising in industrial program verification

Revisiting Synthesis for One-Counter Automata

We study the (parameter) synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables called parameters. The synthesis problem for such automata asks whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some omega-regular property. Lechner showed that (the complement of) the problem can be encoded in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment, called AERPADPLUS, is unfortunately undecidable. Nevertheless, by a careful re-encoding of the problem into a decidable restriction of AERPADPLUS, (ii) we prove that the synthesis problem is decidable in general and in N2EXP for several fixed omega-regular properties. Finally, (iii) we give a polynomial-space algorithm for the special case of the problem where parameters can only be used in tests, and not updates, of the counter

Linear Encodings of Bounded LTL Model Checking

We consider the problem of bounded model checking (BMC) for linear temporal logic (LTL). We present several efficient encodings that have size linear in the bound. Furthermore, we show how the encodings can be extended to LTL with past operators (PLTL). The generalised encoding is still of linear size, but cannot detect minimal length counterexamples. By using the virtual unrolling technique minimal length counterexamples can be captured, however, the size of the encoding is quadratic in the specification. We also extend virtual unrolling to Buchi automata, enabling them to accept minimal length counterexamples. Our BMC encodings can be made incremental in order to benefit from incremental SAT technology. With fairly small modifications the incremental encoding can be further enhanced with a termination check, allowing us to prove properties with BMC. Experiments clearly show that our new encodings improve performance of BMC considerably, particularly in the case of the incremental encoding, and that they are very competitive for finding bugs. An analysis of the liveness-to-safety transformation reveals many similarities to the BMC encodings in this paper. Using the liveness-to-safety translation with BDD-based invariant checking results in an efficient method to find shortest counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005 special issu

Stratified Negation in Limit Datalog Programs

There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing declarative languages for data analysis can be formalised as variants of logic programming equipped with arithmetic function symbols and/or aggregation, and are typically undecidable. In prior work, the language of $\mathit{limit\ programs}$ was proposed, which is sufficiently powerful to capture many analysis tasks and has decidable entailment problem. Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure. We show that the additional expressive power makes reasoning computationally more demanding, and provide tight data complexity bounds. We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.Comment: 14 pages; full version of a paper accepted at IJCAI-1