70 research outputs found
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
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
Refinement Modal Logic
In this paper we present {\em refinement modal logic}. A refinement is like a
bisimulation, except that from the three relational requirements only `atoms'
and `back' need to be satisfied. Our logic contains a new operator 'all' in
addition to the standard modalities 'box' for each agent. The operator 'all'
acts as a quantifier over the set of all refinements of a given model. As a
variation on a bisimulation quantifier, this refinement operator or refinement
quantifier 'all' can be seen as quantifying over a variable not occurring in
the formula bound by it. The logic combines the simplicity of multi-agent modal
logic with some powers of monadic second-order quantification. We present a
sound and complete axiomatization of multi-agent refinement modal logic. We
also present an extension of the logic to the modal mu-calculus, and an
axiomatization for the single-agent version of this logic. Examples and
applications are also discussed: to software verification and design (the set
of agents can also be seen as a set of actions), and to dynamic epistemic
logic. We further give detailed results on the complexity of satisfiability,
and on succinctness
Reasoning about Knowledge and Strategies: Epistemic Strategy Logic
In this paper we introduce Epistemic Strategy Logic (ESL), an extension of
Strategy Logic with modal operators for individual knowledge. This enhanced
framework allows us to represent explicitly and to reason about the knowledge
agents have of their own and other agents' strategies. We provide a semantics
to ESL in terms of epistemic concurrent game models, and consider the
corresponding model checking problem. We show that the complexity of model
checking ESL is not worse than (non-epistemic) Strategy LogicComment: In Proceedings SR 2014, arXiv:1404.041
A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
Interval Temporal Logic (ITL) is an established temporal formalism for
reasoning about time periods. For over 25 years, it has been applied in a
number of ways and several ITL variants, axiom systems and tools have been
investigated. We solve the longstanding open problem of finding a complete
axiom system for basic quantifier-free propositional ITL (PITL) with infinite
time for analysing nonterminating computational systems. Our completeness proof
uses a reduction to completeness for PITL with finite time and conventional
propositional linear-time temporal logic. Unlike completeness proofs of equally
expressive logics with nonelementary computational complexity, our semantic
approach does not use tableaux, subformula closures or explicit deductions
involving encodings of omega automata and nontrivial techniques for
complementing them. We believe that our result also provides evidence of the
naturalness of interval-based reasoning
Realizing Omega-regular Hyperproperties
We studied the hyperlogic HyperQPTL, which combines the concepts of trace
relations and -regularity. We showed that HyperQPTL is very expressive,
it can express properties like promptness, bounded waiting for a grant,
epistemic properties, and, in particular, any -regular property. Those
properties are not expressible in previously studied hyperlogics like HyperLTL.
At the same time, we argued that the expressiveness of HyperQPTL is optimal in
a sense that a more expressive logic for -regular hyperproperties would
have an undecidable model checking problem. We furthermore studied the
realizability problem of HyperQPTL. We showed that realizability is decidable
for HyperQPTL fragments that contain properties like promptness. But still, in
contrast to the satisfiability problem, propositional quantification does make
the realizability problem of hyperlogics harder. More specifically, the
HyperQPTL fragment of formulas with a universal-existential propositional
quantifier alternation followed by a single trace quantifier is undecidable in
general, even though the projection of the fragment to HyperLTL has a decidable
realizability problem. Lastly, we implemented the bounded synthesis problem for
HyperQPTL in the prototype tool BoSy. Using BoSy with HyperQPTL specifications,
we have been able to synthesize several resource arbiters. The synthesis
problem of non-linear-time hyperlogics is still open. For example, it is not
yet known how to synthesize systems from specifications given in branching-time
hyperlogics like HyperCTL.Comment: International Conference on Computer Aided Verification (CAV 2020
Good-for-Game QPTL: An Alternating Hodges Semantics
An extension of QPTL is considered where functional dependencies among the
quantified variables can be restricted in such a way that their current values
are independent of the future values of the other variables. This restriction
is tightly connected to the notion of behavioral strategies in game-theory and
allows the resulting logic to naturally express game-theoretic concepts. The
fragment where only restricted quantifications are considered, called
behavioral quantifications, can be decided, for both model checking and
satisfiability, in 2ExpTime and is expressively equivalent to QPTL, though
significantly less succinct
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