81,320 research outputs found
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
On Optimization Modulo Theories, MaxSMT and Sorting Networks
Optimization Modulo Theories (OMT) is an extension of SMT which allows for
finding models that optimize given objectives. (Partial weighted) MaxSMT --or
equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a
very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT
or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of
state-of-the-art MAXSAT solvers, but they are specific-purpose and not always
applicable; OMT-based approaches are general-purpose, but they suffer from
intrinsic inefficiencies on MaxSMT/OMT+PB problems.
We identify a major source of such inefficiencies, and we address it by
enhancing OMT by means of bidirectional sorting networks. We implemented this
idea on top of the OptiMathSAT OMT solver. We run an extensive empirical
evaluation on a variety of problems, comparing MaxSAT-based and OMT-based
techniques, with and without sorting networks, implemented on top of
OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and
provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1
Hardness measures and resolution lower bounds
Various "hardness" measures have been studied for resolution, providing
theoretical insight into the proof complexity of resolution and its fragments,
as well as explanations for the hardness of instances in SAT solving. In this
report we aim at a unified view of a number of hardness measures, including
different measures of width, space and size of resolution proofs. We also
extend these measures to all clause-sets (possibly satisfiable).Comment: 43 pages, preliminary version (yet the application part is only
sketched, with proofs missing
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