SAT-based Explicit LTL Reasoning

We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly outperforms all existing LTL satisfiability solvers. Furthermore, we show that the framework can be extended from propositional LTL to assertional LTL (where we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and demonstrating that this can yield an exponential improvement in performance

SAT-based Explicit LTLf Satisfiability Checking

We present here a SAT-based framework for LTLf (Linear Temporal Logic on Finite Traces) satisfiability checking. We use propositional SAT-solving techniques to construct a transition system for the input LTLf formula; satisfiability checking is then reduced to a path-search problem over this transition system. Furthermore, we introduce CDLSC (Conflict-Driven LTLf Satisfiability Checking), a novel algorithm that leverages information produced by propositional SAT solvers from both satisfiability and unsatisfiability results. Experimental evaluations show that CDLSC outperforms all other existing approaches for LTLf satisfiability checking, by demonstrating an approximate four-fold speedup compared to the second-best solver

Improving MCS Enumeration via Caching

Enumeration of minimal correction sets (MCSes) of conjunctive normal form formulas is a central and highly intractable problem in infeasibility analysis of constraint systems. Often complete enumeration of MCSes is impossible due to both high computational cost and worst-case exponential number of MCSes. In such cases partial enumeration is sought for, finding applications in various domains, including axiom pinpointing in description logics among others. In this work we propose caching as a means of further improving the practical efficiency of current MCS enumeration approaches, and show the potential of caching via an empirical evaluation.Peer reviewe

Finding Unsatisfiable Subformulas with Stochastic Method

Abstract. Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. A small unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. In recent years the problem of finding unsatisfiable subformulas has been addressed frequently by research works, which are mostly based on the SAT solvers with DPLL backtrack-search algorithm. However little attention has been concentrated on extraction of unsatisfiable subformulas using stochastic methods. In this paper, we propose a resolution-based stochastic local search algorithm to derive unsatisfiable subformulas. This approach directly constructs the resolution sequences for proving unsatisfiability with a local search procedure, and then extracts small unsatisfiable subformulas from the refutation traces. We report and analyze the experimental results on benchmarks

Using Local Search to Find \MSSes and MUSes

International audienceIn this paper, a new complete technique to compute Maximal Satisfiable Subsets (MSSes) and Minimally Unsatisfiable Subformulas (MUSes) of sets of Boolean clauses is introduced. The approach improves the currently most efficient complete technique in several ways. It makes use of the powerful concept of critical clause and of a computationally inexpensive local search oracle to boost an exhaustive algorithm proposed by Liffiton and Sakallah. These features can allow exponential efficiency gains to be obtained. Accordingly, experimental studies show that this new approach outperforms the best current existing exhaustive ones