1,958 research outputs found
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
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)
Combining Spatial and Temporal Logics: Expressiveness vs. Complexity
In this paper, we construct and investigate a hierarchy of spatio-temporal
formalisms that result from various combinations of propositional spatial and
temporal logics such as the propositional temporal logic PTL, the spatial
logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a
clear picture of the trade-off between expressiveness and computational
realisability within the hierarchy. We demonstrate how different combining
principles as well as spatial and temporal primitives can produce NP-, PSPACE-,
EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out
of components that are at most NP- or PSPACE-complete
On the Hybrid Extension of CTL and CTL+
The paper studies the expressivity, relative succinctness and complexity of
satisfiability for hybrid extensions of the branching-time logics CTL and CTL+
by variables. Previous complexity results show that only fragments with one
variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the
hybrid extensions with one variable of CTL+ and CTL, respectively, are
expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL.
On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many
variables does not capture CTL*, as it even cannot express the simple CTL*
property EGFp. The satisfiability problem for H1CTL+ is complete for triply
exponential time, this remains true for quite weak fragments and quite strong
extensions of the logic
One-pass Context-based Tableaux Systems for CTL and ECTL
When building tableau for temporal logic formulae, applying a two-pass construction, we first check the validity of the given tableaux input by creating a tableau graph, and then, in the second `pass', we check if all the eventualities are satisfied. In one-pass tableaux checking the validity of the input does not require these auxiliary constructions. This paper continues the development of one-pass tableau method for temporal logics introducing tree-style one-pass tableau systems for Computation Tree Logic (CTL) and shows how this can be extended to capture Extended CTL (ECTL). A distinctive feature here is the utilisation, for the core tableau construction, of the concept of a context of an eventuality which forces its earliest fulfilment. Relevant algorithms for obtaining a systematic tableau for these branching-time logics are also defined. We prove the soundness and completeness of the method. With these developments of a tree-shaped one-pass tableau for CTL and ECTL, we have formalisms which are well suited for the automation and are amenable for the implementation, and for the formulation of dual sequent calculi. This brings us one step closer to the application of one pass context based tableaux in certified model checking for a variety of CTL-type branching-time logics
Interrupt Timed Automata: verification and expressiveness
We introduce the class of Interrupt Timed Automata (ITA), a subclass of
hybrid automata well suited to the description of timed multi-task systems with
interruptions in a single processor environment. While the reachability problem
is undecidable for hybrid automata we show that it is decidable for ITA. More
precisely we prove that the untimed language of an ITA is regular, by building
a finite automaton as a generalized class graph. We then establish that the
reachability problem for ITA is in NEXPTIME and in PTIME when the number of
clocks is fixed. To prove the first result, we define a subclass ITA- of ITA,
and show that (1) any ITA can be reduced to a language-equivalent automaton in
ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without
any class graph). In the next step, we investigate the verification of real
time properties over ITA. We prove that model checking SCL, a fragment of a
timed linear time logic, is undecidable. On the other hand, we give model
checking procedures for two fragments of timed branching time logic. We also
compare the expressive power of classical timed automata and ITA and prove that
the corresponding families of accepted languages are incomparable. The result
also holds for languages accepted by controlled real-time automata (CRTA), that
extend timed automata. We finally combine ITA with CRTA, in a model which
encompasses both classes and show that the reachability problem is still
decidable. Additionally we show that the languages of ITA are neither closed
under complementation nor under intersection
Interval Temporal Logic for Visibly Pushdown Systems
In this paper, we introduce and investigate an extension of Halpern and Shoham\u27s interval temporal logic HS for the specification and verification of branching-time context-free requirements of pushdown systems under a state-based semantics over Kripke structures. Both homogeneity and visibility are assumed. The proposed logic, called nested BHS, supports branching-time both in the past and in the future, and is able to express non-regular properties of linear and branching behaviours of procedural contexts in a natural way. It strictly subsumes well-known linear time context-free extensions of LTL such as CaRet [R. Alur et al., 2004] and NWTL [R. Alur et al., 2007]. The main result is the decidability of the visibly pushdown model-checking problem against nested BHS. The proof exploits a non-trivial automata-theoretic construction
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
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