20 research outputs found
Embedding Session Types in HML
Recent work on the enhancement of multiparty session types with logical annotations enable the effective verification of properties on (1) the structure of the conversations, (2) the sorts of the messages, and (3) the actual values exchanged. In [3] we extend this work to enable the specification and verification of mutual effects of multiple cross-session interactions. Here we give a sound and complete embedding into the Hennessy-Milner logic to justify the expressiveness of the approach in [3] and to provide it with a logical background that will enable us to compare it with similar approaches
Ockhamist Propositional Dynamic Logic: a natural link between PDL and CTL
International audienceWe present a new logic called Ockhamist Propositional Dynamic Logic, OPDL, which provides a natural link between PDL and CTL*. We show that both PDL and CTL* can be polynomially embedded into OPDL in a rather simple and direct way. More generally, the semantics on which OPDL is based provides a unifying framework for making the dynamic logic family and the temporal logic family converge in a single logical framework. Decidability of the satisfiability problem for OPDL is studied in the paper
Sampling-based motion planning with deterministic u-calculus specifications
In this paper, we propose algorithms for the online
computation of control programs for dynamical systems
that provably satisfy a class of temporal logic specifications.
Such specifications have recently been proposed in the literature
as a powerful tool to synthesize provably correct
control programs, for example for embedded systems and
robotic applications. The proposed algorithms, generalizing
state-of-the-art algorithms for point-to-point motion planning,
incrementally build finite transition systems representing a
discrete subset of dynamically feasible trajectories. At each
iteration, local -calculus model-checking methods are used
to establish whether the current transition system satisfies
the specifications. Efficient sampling strategies are presented,
ensuring the probabilistic completeness of the algorithms. We
demonstrate the effectiveness of the proposed approach on
simulation examples.Michigan/AFRL Collaborative Center on Control Sciences, AFOSR (grant no. FA 8650-07-2-3744
Static Analysis of Parity Games: Alternating Reachability Under Parity
It is well understood that solving parity games is equivalent, up to polynomial time, to model checking of the modal mu-calculus. It is a long-standing open problem whether solving parity games (or model checking modal mu-calculus formulas) can be done in polynomial time. A recent approach to studying this problem has been the design of partial solvers, algorithms that run in polynomial time and that may only solve parts of a parity game. Although it was shown that such partial solvers can completely solve many practical benchmarks, the design of such partial solvers was somewhat ad hoc, limiting a deeper understanding of the potential of that approach. We here mean to provide such robust foundations for deeper analysis through a new form of game, alternating reachability under parity. We prove the determinacy of these games and use this determinacy to define, for each player, a monotone fixed point over an ordered domain of height linear in the size of the parity game such that all nodes in its greatest fixed point are won by said player in the parity game. We show, through theoretical and experimental work, that such greatest fixed points and their computation leads to partial solvers that run in polynomial time. These partial solvers are based on established principles of static analysis and are more effective than partial solvers studied in extant work
Static analysis of parity games: alternating reachability under parity
It is well understood that solving parity games is equivalent, up to polynomial time, to model checking of the modal mu-calculus. It is a long-standing open problem whether solving parity games (or model checking modal mu-calculus formulas) can be done in polynomial time. A recent approach to studying this problem has been the design of partial solvers, algorithms that run in polynomial time and that may only solve parts of a parity game. Although it was shown that such partial solvers can completely solve many practical benchmarks, the design of such partial solvers was somewhat ad hoc, limiting a deeper understanding of the potential of that approach. We here mean to provide such robust foundations for deeper analysis through a new form of game, alternating reachability under parity. We prove the determinacy of these games and use this determinacy to define, for each player, a monotone fixed point over an ordered domain of height linear in the size of the parity game such that all nodes in its greatest fixed point are won by said player in the parity game. We show, through theoretical and experimental work, that such greatest fixed points and their computation leads to partial solvers that run in polynomial time. These partial solvers are based on established principles of static analysis and are more effective than partial solvers studied in extant work
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53