2,967 research outputs found
PrIC3: Property Directed Reachability for MDPs
IC3 has been a leap forward in symbolic model checking. This paper proposes
PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic
model checking of MDPs. Our main focus is to develop the theory underlying
PrIC3. Alongside, we present a first implementation of PrIC3 including the key
ingredients from IC3 such as generalization, repushing, and propagation
Abstraction and probabilities for hybrid logics
We suggest and develop mathematical foundations for quantitative versions of hybrid logics by means of two related themes: a relational abstraction technique for hybrid computation tree logic and hybrid Kripke structures as an extension of the model-checking framework for computation tree logic with the ability to name, bind, and retrieve states; and a syntax and semantics for hybrid probabilistic computation tree logic over hybrid extensions of labelled Markov chains for which the relational abstraction techniques of hybrid Kripke structures should be transferable
Counterexample Generation in Probabilistic Model Checking
Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol
Counterexample Guided Abstraction Refinement with Non-Refined Abstractions for Multi-Agent Path Finding
Counterexample guided abstraction refinement (CEGAR) represents a powerful
symbolic technique for various tasks such as model checking and reachability
analysis. Recently, CEGAR combined with Boolean satisfiability (SAT) has been
applied for multi-agent path finding (MAPF), a problem where the task is to
navigate agents from their start positions to given individual goal positions
so that the agents do not collide with each other.
The recent CEGAR approach used the initial abstraction of the MAPF problem
where collisions between agents were omitted and were eliminated in subsequent
abstraction refinements. We propose in this work a novel CEGAR-style solver for
MAPF based on SAT in which some abstractions are deliberately left non-refined.
This adds the necessity to post-process the answers obtained from the
underlying SAT solver as these answers slightly differ from the correct MAPF
solutions. Non-refining however yields order-of-magnitude smaller SAT encodings
than those of the previous approach and speeds up the overall solving process
making the SAT-based solver for MAPF competitive again in relevant benchmarks
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