572 research outputs found
Parity Games on Temporal Graphs
Temporal graphs are a popular modelling mechanism for dynamic complex systems
that extend ordinary graphs with discrete time. Simply put, time progresses one
unit per step and the availability of edges can change with time. We consider
the complexity of solving -regular games played on temporal graphs
where the edge availability is ultimately periodic and fixed a priori.
We show that solving parity games on temporal graphs is decidable in PSPACE,
only assuming the edge predicate itself is in PSPACE. A matching lower bound
already holds for what we call punctual reachability games on static graphs,
where one player wants to reach the target at a given, binary encoded, point in
time. We further study syntactic restrictions that imply more efficient
procedures. In particular, if the edge predicate is in and is monotonically
increasing for one player and decreasing for the other, then the complexity of
solving games is only polynomially increased compared to static graphs
LNCS
We solve the offline monitoring problem for timed propositional temporal logic (TPTL), interpreted over dense-time Boolean signals. The variant of TPTL we consider extends linear temporal logic (LTL) with clock variables and reset quantifiers, providing a mechanism to specify real-time constraints. We first describe a general monitoring algorithm based on an exhaustive computation of the set of satisfying clock assignments as a finite union of zones. We then propose a specialized monitoring algorithm for the one-variable case using a partition of the time domain based on the notion of region equivalence, whose complexity is linear in the length of the signal, thereby generalizing a known result regarding the monitoring of metric temporal logic (MTL). The region and zone representations of time constraints are known from timed automata verification and can also be used in the discrete-time case. Our prototype implementation appears to outperform previous discrete-time implementations of TPTL monitoring
Reachability analysis for timed automata using max-plus algebra
International audienceWe show that max-plus polyhedra are usable as a data structure in reachability analysis of timed automata. Drawing inspiration from the extensive work that has been done on difference bound matrices, as well as previous work on max-plus polyhedra in other areas, we develop the algorithms needed to perform forward and backward reachability analysis using max-plus polyhedra. To show that the approach works in practice and theory alike, we have created a proof-of-concept implementation on top of the model checker opaal
Oink: an Implementation and Evaluation of Modern Parity Game Solvers
Parity games have important practical applications in formal verification and
synthesis, especially to solve the model-checking problem of the modal
mu-calculus. They are also interesting from the theory perspective, as they are
widely believed to admit a polynomial solution, but so far no such algorithm is
known. In recent years, a number of new algorithms and improvements to existing
algorithms have been proposed. We implement a new and easy to extend tool Oink,
which is a high-performance implementation of modern parity game algorithms. We
further present a comprehensive empirical evaluation of modern parity game
algorithms and solvers, both on real world benchmarks and randomly generated
games. Our experiments show that our new tool Oink outperforms the current
state-of-the-art.Comment: Accepted at TACAS 201
- …