8,329 research outputs found
Concurrent program schemes and their logics
AbstractWe define and investigate several classes of concurrent program schemes, including goto schemes and two versions of structured schemes, based on extensions of the regular expressions to trees. The schemes are studied on the first-order, Boolean-variable and propositional levels. We also define and study the dynamic logics based on these classes of schemes, including issues of decidability and axiomatization
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
Reasoning About Strategies: On the Model-Checking Problem
In open systems verification, to formally check for reliability, one needs an
appropriate formalism to model the interaction between agents and express the
correctness of the system no matter how the environment behaves. An important
contribution in this context is given by modal logics for strategic ability, in
the setting of multi-agent games, such as ATL, ATL\star, and the like.
Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which
we denote here by CHP-SL, with the aim of getting a powerful framework for
reasoning explicitly about strategies. CHP-SL is obtained by using first-order
quantifications over strategies and has been investigated in the very specific
setting of two-agents turned-based games, where a non-elementary model-checking
algorithm has been provided. While CHP-SL is a very expressive logic, we claim
that it does not fully capture the strategic aspects of multi-agent systems. In
this paper, we introduce and study a more general strategy logic, denoted SL,
for reasoning about strategies in multi-agent concurrent games. We prove that
SL includes CHP-SL, while maintaining a decidable model-checking problem. In
particular, the algorithm we propose is computationally not harder than the
best one known for CHP-SL. Moreover, we prove that such a problem for SL is
NonElementarySpace-hard. This negative result has spurred us to investigate
here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of
obtaining an elementary model-checking problem. Among the others, we study the
sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special
prenex normal form having, respectively, nested temporal goals, Boolean
combinations of goals and, a single goal at a time. About these logics, we
prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not
harder than the one for ATL\star
A Temporal Logic for Hyperproperties
Hyperproperties, as introduced by Clarkson and Schneider, characterize the
correctness of a computer program as a condition on its set of computation
paths. Standard temporal logics can only refer to a single path at a time, and
therefore cannot express many hyperproperties of interest, including
noninterference and other important properties in security and coding theory.
In this paper, we investigate an extension of temporal logic with explicit path
variables. We show that the quantification over paths naturally subsumes other
extensions of temporal logic with operators for information flow and knowledge.
The model checking problem for temporal logic with path quantification is
decidable. For alternation depth 1, the complexity is PSPACE in the length of
the formula and NLOGSPACE in the size of the system, as for linear-time
temporal logic
Simplifying Inductive Schemes in Temporal Logic
In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula
Communication in concurrent dynamic logic
AbstractCommunication mechanisms are introduced into the program schemes of Concurrent Dynamic Logic, on both the propositional and the first-order levels. The effects of these mechanisms (particularly, channels, shared variables, and “message collectors”) on issues of expressiveness and decidability are investigated. In general, we find that both respects are dominated by the extent to which the capabilities of synchronization and (unbounded counting are enabled in the communication scheme
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