110 research outputs found
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
We show that Branching-time temporal logics CTL and CTL*, as well as
Alternating-time temporal logics ATL and ATL*, are as semantically expressive
in the language with a single propositional variable as they are in the full
language, i.e., with an unlimited supply of propositional variables. It follows
that satisfiability for CTL, as well as for ATL, with a single variable is
EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a
single variable is 2EXPTIME-complete,--i.e., for these logics, the
satisfiability for formulas with only one variable is as hard as satisfiability
for arbitrary formulas.Comment: Prefinal version of the published pape
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
On the Complexity of ATL and ATL* Module Checking
Module checking has been introduced in late 1990s to verify open systems,
i.e., systems whose behavior depends on the continuous interaction with the
environment. Classically, module checking has been investigated with respect to
specifications given as CTL and CTL* formulas. Recently, it has been shown that
CTL (resp., CTL*) module checking offers a distinctly different perspective
from the better-known problem of ATL (resp., ATL*) model checking. In
particular, ATL (resp., ATL*) module checking strictly enhances the
expressiveness of both CTL (resp., CTL*) module checking and ATL (resp. ATL*)
model checking. In this paper, we provide asymptotically optimal bounds on the
computational cost of module checking against ATL and ATL*, whose upper bounds
are based on an automata-theoretic approach. We show that module-checking for
ATL is EXPTIME-complete, which is the same complexity of module checking
against CTL. On the other hand, ATL* module checking turns out to be
3EXPTIME-complete, hence exponentially harder than CTL* module checking.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
Optimal Tableaux Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-time Temporal Logic ATL+
We develop a sound, complete and practically implementable tableaux-based
decision method for constructive satisfiability testing and model synthesis in
the fragment ATL+ of the full Alternating time temporal logic ATL*. The method
extends in an essential way a previously developed tableaux-based decision
method for ATL and works in 2EXPTIME, which is the optimal worst case
complexity of the satisfiability problem for ATL+ . We also discuss how
suitable parametrizations and syntactic restrictions on the class of input ATL+
formulae can reduce the complexity of the satisfiability problem.Comment: 45 page
Robust Alternating-Time Temporal Logic
In multi-agent system design, a crucial aspect is to ensure robustness,
meaning that for a coalition of agents A, small violations of adversarial
assumptions only lead to small violations of A's goals. In this paper we
introduce a logical framework for robust strategic reasoning about multi-agent
systems. Specifically, inspired by recent works on robust temporal logics, we
introduce and study rATL and rATL*, logics that extend the well-known
Alternating-time Temporal Logic ATL and ATL* by means of an opportune
multi-valued semantics for the strategy quantifiers and temporal operators. We
study the model-checking and satisfiability problems for rATL and rATL* and
show that dealing with robustness comes at no additional computational cost.
Indeed, we show that these problems are PTime-complete and ExpTime-complete for
rATL, respectively, while both are 2ExpTime-complete for rATL*
Reasoning about actions meets strategic logics (LORI 2013)
International audienceWe introduce ATLEA, a novel extension of Alternating-time Temporal Logic with explicit actions in the object language. ATLEA allows to reason about abilities of agents under commitments to play certain actions. Pre- and postconditions as well as availability and unavailability of actions can be expressed. We show that the multiagent extension of Reiter’s solution to the frame problem can be encoded into ATLEA. We also consider an epistemic extension of ATLEA. We demonstrate that the resulting logic is sufficiently expressive to reason about uniform choices of actions. Complexity results for the satisfiability problem of ATLEA and its epistemic extension are given in the paper
Optimal Decision Procedures for Satisfiability in Fragments of Alternating-time Temporal Logics
We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and ATL are
-complete. We note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities
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