Probabilistic Satisfiability: Logic-Based Algorithms and Phase Transition
نویسندگان
چکیده
In this paper, we study algorithms for probabilistic satisfiability (PSAT), an NP-complete problem, and their empiric complexity distribution. We define a PSAT normal form, based on which we propose two logic-based algorithms: a reduction of normal form PSAT instances to SAT, and a linearalgebraic algorithm with a logic-based column generation strategy. We conclude that both algorithms present a phase transition behaviour and that the latter has a much better performance. We discuss the role of logic and the normal form in the detection of the phase transition.
منابع مشابه
Classical Generalized Probabilistic Satisfiability
We analyze a classical generalized probabilistic satisfiability problem (GGenPSAT) which consists in deciding the satisfiability of Boolean combinations of linear inequalities involving probabilities of classical propositional formulas. GGenPSAT coincides precisely with the satisfiability problem of the probabilistic logic of Fagin et al. and was proved to be NP-complete. Here, we present a pol...
متن کاملPhase Transitions in Classical Planning: An Experimental Study
Phase transitions in the solubility of problem instances are known in many types of computational problems relevant for artificial intelligence, most notably for the satisfiability problem of the classical propositional logic. However, phase transitions in classical planning have received far less attention. Bylander has investigated phase transitions theoretically as well as experimentally by ...
متن کاملProbabilistic Mu-Calculus: Decidability and Complete Axiomatization
We introduce a version of the probabilistic μ-calculus (PMC) built on top of a probabilistic modal logic that allows encoding n-ary inequational conditions on transition probabilities. PMC extends previously studied calculi and we prove that, despite its expressiveness, it enjoys a series of good metaproperties. Firstly, we prove the decidability of satisfiability checking by establishing the s...
متن کاملProbabilistic Satisfiability and Coherence Checking through Integer Programming
This paper presents algorithms based on integer programming, both for probabilistic satisfiability and coherence checking. That is, we consider probabilistic assessments for both standard probability measures (Kolmogorovian setup) and full conditional measures (de Finettian coherence setup), and in both cases verify satisfiability/coherence using integer programming. We present empirical evalua...
متن کاملProbabilistic Greedy Heuristics for Satisfiability Problems
We examine probabilistic greedy heuristics for maximization and minimization versions of the satisfiability problem. Like deterministic greedy algorithms, these heuristics construct a truth assignment one variable at a time. Unlike them, they set a variable true or false using a probabilistic mechanism, the probabilities of a true assignment depending on the incremental number of clauses satisf...
متن کامل