3,004 research outputs found
Model-Checking Counting Temporal Logics on Flat Structures
We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show that decidability can be recovered by considering flat Kripke structures where each state belongs to at most one simple loop. Most decision procedures are based on results on (flat) counter systems where counters are used to implement the evaluation of counting operators
From Quantified CTL to QBF
QCTL extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as MSO). Several semantics exist for the quantifications: here, we work with the structure semantics, where the extra propositions label the Kripke structure (and not its execution tree), and the model-checking problem is known to be PSPACE-complete in this framework. We propose a model-checking algorithm for QCTL based on a reduction to QBF. We consider several reduction strategies, and we compare them with a prototype (based on the SMT-solver Z3) on several examples
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Bounded Reachability for Temporal Logic over Constraint Systems
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future
operators) augmented with atomic formulae built over a constraint system D.
Even for decidable constraint systems, satisfiability and Model Checking
problem of such logic can be undecidable. We introduce suitable restrictions
and assumptions that are shown to make the satisfiability problem for the
extended logic decidable. Moreover for a large class of constraint systems we
propose an encoding that realize an effective decision procedure for the
Bounded Reachability problem
Flat Model Checking for Counting LTL Using Quantifier-Free Presburger Arithmetic
This paper presents an approximation approach to verifying counter systems
with respect to properties formulated in an expressive counting extension of
linear temporal logic. It can express, e.g., that the number of
acknowledgements never exceeds the number of requests to a service, by counting
specific positions along a run and imposing arithmetic constraints. The
addressed problem is undecidable and therefore solved on flat
under-approximations of a system. This provides a flexibly adjustable trade-off
between exhaustiveness and computational effort, similar to bounded model
checking. Recent techniques and results for model-checking frequency properties
over flat Kripke structures are lifted and employed to construct a parametrised
encoding of the (approximated) problem in quantifier-free Presburger
arithmetic. A prototype implementation based on the z3 SMT solver demonstrates
the effectiveness of the approach based on problems from the RERS Challange
Constraint LTL Satisfiability Checking without Automata
This paper introduces a novel technique to decide the satisfiability of
formulae written in the language of Linear Temporal Logic with Both future and
past operators and atomic formulae belonging to constraint system D (CLTLB(D)
for short). The technique is based on the concept of bounded satisfiability,
and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of
quantifier-free equality and uninterpreted functions combined with D. Similarly
to standard LTL, where bounded model-checking and SAT-solvers can be used as an
alternative to automata-theoretic approaches to model-checking, our approach
allows users to solve the satisfiability problem for CLTLB(D) formulae through
SMT-solving techniques, rather than by checking the emptiness of the language
of a suitable automaton A_{\phi}. The technique is effective, and it has been
implemented in our Zot formal verification tool.Comment: 39 page
- …