5,689 research outputs found
A Logical Characterization of Timed (non-)Regular Languages
CLTLoc (Constraint LTL over clocks) is a quantifier-free extension of LTL allowing variables behaving like clocks over real numbers. CLTLoc is in PSPACE [9] and its satisfiability can polynomially be reduced to a SMT problem, allowing a feasible implementation of a decision procedure. We used CLTLoc to capture the semantics of metric temporal logics over continuous time, such as Metric Interval Temporal Logic (MITL), resulting in the first successful implementation of a tool for checking MITL satisfiability [7]. In this paper, we assess the expressive power of CLTLoc, by comparing it with various temporal formalisms over dense time.When interpreted over timed words, CLTLoc is equivalent to Timed Automata. We also define a monadic theory of orders, extending the one introduced by Kamp, which is expressively equivalent to CLTLoc. We investigate a decidable extension with an arithmetical next operator, which allows the expression of timed non-ω-regular languages
Automaten und Logiken zur Beschreibung zeitabhängiger Systeme
When speaking of a 'real-time system' we are interested in a system's evolution in time where time is viewed as linear and measured in terms of non-negative real numbers. The thesis deals with automata-theoretic models of real-time systems and their description in monadic second-order and temporal logics. A parametrized automaton model is introduced and for this model a logical description in terms of a family of existential monadic second-order logics is obtained. This characterization is used to give a logical description of the behaviour of well-known models of real-time systems: timed automata (Alur & Dill), timed automata with halting feature, and linear hybrid automata. The corresponding logics incorporate distance, duration, and integration formulas, respectively. For instance, timed automata are captured by the {\em monadic logic of relative distance.} Its signature contains for every relation symbol ~ such as =, , , or and every natural number k a binary predicate d(.,.)~k taking a set of natural numbers and a single natural number as arguments. The atomic formula d(X,y)~k is true in a timed state sequence if X contains a position smaller than y and the distance (in time) between position y and the last position before y that belongs to X satisfies the condition ~k. The monadic logic of relative distance turns out to have two important properties. First, its satisfiability problem is decidable, for its equivalence to timed automata allows a reduction of the satisfiability problem to the emptiness problem for such automata and this, in turn, is decidable due to Alur and Dill. Second, the monadic logic of relative distance is a powerful logic. One evidence for this is given by showing that the logic is strictly more expressive than the most powerful logic (for the specification of real-time systems) previously known to be decidable, namely the logic MITL^P introduced by Alur and Henzinger. By effectively embedding the latter logic in the former an alternative proof of Alur's and Henzinger's decidability result concerning MITL^P is obtained. Using embedding techniques also the decidability of Manna's and Pnueli's logic TL_Gamma is proved. Timed automata and the languages recognised by them, the so-called timed regular languages, are analysed in more detail. Several aspects are considered. A pumping lemma for timed automata is given, resulting in a formal proof that timed regular languages are not closed under complementation. It is shown that the number of clocks used in timed automata gives rise to an infinite hierarchy of timed regular languages, that the minimal number of clocks required for the recognition of a timed regular language is not computable, and that the property of a two-way timed automaton (Alur & Henzinger) to be reversal bounded is undecidable. Furthermore, unambiguous timed automata are considered, and an inherently ambiguous language is presented. Finally, variations of the emptiness problem for the three types of automata aforementioned and different restrictions concerning the event duration (bounded variation, minimal duration, and unit duration) are discussed. In particular, it is shown that bounded variation leads to a decidable emptiness problem in the case of timed automata, which implies that the full monadic logic of distance is decidable when restricted to timed state sequences of bounded variation. The obtained undecidability results give evidence that the monadic logic of relative distance is a good choice with respect to expressiveness and the requirement of a decidable satisfiability problem
Logic Meets Algebra: the Case of Regular Languages
The study of finite automata and regular languages is a privileged meeting
point of algebra and logic. Since the work of Buchi, regular languages have
been classified according to their descriptive complexity, i.e. the type of
logical formalism required to define them. The algebraic point of view on
automata is an essential complement of this classification: by providing
alternative, algebraic characterizations for the classes, it often yields the
only opportunity for the design of algorithms that decide expressibility in
some logical fragment.
We survey the existing results relating the expressibility of regular
languages in logical fragments of MSO[S] with algebraic properties of their
minimal automata. In particular, we show that many of the best known results in
this area share the same underlying mechanics and rely on a very strong
relation between logical substitutions and block-products of pseudovarieties of
monoid. We also explain the impact of these connections on circuit complexity
theory.Comment: 37 page
Challenges in Timed Languages: From Applied Theory to Basic Theory
The Concurrency Column, by Luca Aceto. Partially based on the invited talk at FORMATS'03 workshopCurrent state and perspectives of development of the theory of timed languages are analyzed. A large list of open problems is suggested
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Timed pushdown automata revisited
This paper contains two results on timed extensions of pushdown automata
(PDA). As our first result we prove that the model of dense-timed PDA of
Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with
timeless stack. Motivated by this result, we advocate the framework of
first-order definable PDA, a specialization of PDA in sets with atoms, as the
right setting to define and investigate timed extensions of PDA. The general
model obtained in this way is Turing complete. As our second result we prove
NEXPTIME upper complexity bound for the non-emptiness problem for an expressive
subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more
restrictive subclass of PDA with timeless stack, thus subsuming the complexity
bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape
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