9,215 research outputs found
Modal µ-Calculus, Model Checking and Gauß Elimination
In this paper we present a novel approach for solving Boolean equation systems with nested minimal and maximal fixpoints. The method works by successively eliminating variables and reducing a Boolean equation system similar to Gauß elimination for linear equation systems. It does not require backtracking techniques. Within one framework we suggest a global and a local algorithm. In the context of model checking in the modal-calculus the local algorithm is related to the tableau methods, but has a better worst case complexity
Boolean Hedonic Games
We study hedonic games with dichotomous preferences. Hedonic games are
cooperative games in which players desire to form coalitions, but only care
about the makeup of the coalitions of which they are members; they are
indifferent about the makeup of other coalitions. The assumption of dichotomous
preferences means that, additionally, each player's preference relation
partitions the set of coalitions of which that player is a member into just two
equivalence classes: satisfactory and unsatisfactory. A player is indifferent
between satisfactory coalitions, and is indifferent between unsatisfactory
coalitions, but strictly prefers any satisfactory coalition over any
unsatisfactory coalition. We develop a succinct representation for such games,
in which each player's preference relation is represented by a propositional
formula. We show how solution concepts for hedonic games with dichotomous
preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic
and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen,
Norway, July 27-30, 201
SMT-based Model Checking for Recursive Programs
We present an SMT-based symbolic model checking algorithm for safety
verification of recursive programs. The algorithm is modular and analyzes
procedures individually. Unlike other SMT-based approaches, it maintains both
"over-" and "under-approximations" of procedure summaries. Under-approximations
are used to analyze procedure calls without inlining. Over-approximations are
used to block infeasible counterexamples and detect convergence to a proof. We
show that for programs and properties over a decidable theory, the algorithm is
guaranteed to find a counterexample, if one exists. However, efficiency depends
on an oracle for quantifier elimination (QE). For Boolean Programs, the
algorithm is a polynomial decision procedure, matching the worst-case bounds of
the best BDD-based algorithms. For Linear Arithmetic (integers and rationals),
we give an efficient instantiation of the algorithm by applying QE "lazily". We
use existing interpolation techniques to over-approximate QE and introduce
"Model Based Projection" to under-approximate QE. Empirical evaluation on
SV-COMP benchmarks shows that our algorithm improves significantly on the
state-of-the-art.Comment: originally published as part of the proceedings of CAV 2014; fixed
typos, better wording at some place
An Instantiation-Based Approach for Solving Quantified Linear Arithmetic
This paper presents a framework to derive instantiation-based decision
procedures for satisfiability of quantified formulas in first-order theories,
including its correctness, implementation, and evaluation. Using this framework
we derive decision procedures for linear real arithmetic (LRA) and linear
integer arithmetic (LIA) formulas with one quantifier alternation. Our
procedure can be integrated into the solving architecture used by typical SMT
solvers. Experimental results on standardized benchmarks from model checking,
static analysis, and synthesis show that our implementation of the procedure in
the SMT solver CVC4 outperforms existing tools for quantified linear
arithmetic
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