954 research outputs found
Fast LTL Satisfiability Checking by SAT Solvers
Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step
in checking for possible errors in LTL assertions. Extant LTL satisfiability
checkers use a variety of different search procedures. With the sole exception
of LTL satisfiability checking based on bounded model checking, which does not
provide a complete decision procedure, LTL satisfiability checkers have not
taken advantage of the remarkable progress over the past 20 years in Boolean
satisfiability solving. In this paper, we propose a new LTL
satisfiability-checking framework that is accelerated using a Boolean SAT
solver. Our approach is based on the variant of the \emph{obligation-set
method}, which we proposed in earlier work. We describe here heuristics that
allow the use of a Boolean SAT solver to analyze the obligations for a given
LTL formula. The experimental evaluation indicates that the new approach
provides a a significant performance advantage
On Relaxing Metric Information in Linear Temporal Logic
Metric LTL formulas rely on the next operator to encode time distances,
whereas qualitative LTL formulas use only the until operator. This paper shows
how to transform any metric LTL formula M into a qualitative formula Q, such
that Q is satisfiable if and only if M is satisfiable over words with
variability bounded with respect to the largest distances used in M (i.e.,
occurrences of next), but the size of Q is independent of such distances.
Besides the theoretical interest, this result can help simplify the
verification of systems with time-granularity heterogeneity, where large
distances are required to express the coarse-grain dynamics in terms of
fine-grain time units.Comment: Minor change
Fully Observable Non-deterministic Planning as Assumption-Based Reactive Synthesis
We contribute to recent efforts in relating two approaches to automatic synthesis, namely, automated planning and discrete reactive synthesis. First, we develop a declarative characterization of the standard “fairness” assumption on environments in non-deterministic planning, and show that strong-cyclic plans are correct solution concepts for fair environments. This complements, and arguably completes, the existing foundational work on non-deterministic planning, which focuses on characterizing (and computing) plans enjoying special “structural” properties, namely loopy but closed policy structures. Second, we provide an encoding suitable for reactive synthesis that avoids the naive exponential state space blowup. To do so, special care has to be taken to specify the fairness assumption on the environment in a succinct manner.Fil: D'ippolito, Nicolás Roque. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Rodriguez, Natalia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Sardina, Sebastian. RMIT University; Australi
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
LTLf satisfiability checking
We consider here Linear Temporal Logic (LTL) formulas interpreted over
\emph{finite} traces. We denote this logic by LTLf. The existing approach for
LTLf satisfiability checking is based on a reduction to standard LTL
satisfiability checking. We describe here a novel direct approach to LTLf
satisfiability checking, where we take advantage of the difference in the
semantics between LTL and LTLf. While LTL satisfiability checking requires
finding a \emph{fair cycle} in an appropriate transition system, here we need
to search only for a finite trace. This enables us to introduce specialized
heuristics, where we also exploit recent progress in Boolean SAT solving. We
have implemented our approach in a prototype tool and experiments show that our
approach outperforms existing approaches
Model Checking CTL is Almost Always Inherently Sequential
The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations—restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that in most applications, approaching CTL model checking by parallelism will not result in the desired speed up. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL +, and ECTL +
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