On Timed Scope-Bounded Context-Sensitive Languages

International Journal of Applied Information Systems, 2012

In this paper we present durational actions timed automata, DATA*, as a sub class of timed automata. In the contrast of T.A, the underling semantic of DATA* is the maximality semantics which claim that actions have durations and true concurrency is captured differently from choice. DATA* model is in one hand useful for modeling and validating reel aspects of systems. In the other hand, it is determinizable and closed under all Boolean operations. As result, the language inclusion problem is decidable. Then, we compare a durational actions timed automata to event recording automata, which is a determinizable sub class of the classical timed automata. Next, we propose a simple framework to aggregate region of DATA* for reducing its space state. This study is based on an aggregation region automata procedure to reduce the combinatorial explosion of regions. Finally, we discuss equivalence and validation of systems.

Lecture Notes in Computer Science, 2018

In this paper we introduce and study Event-Clock Nested Automata (ECNA), a formalism that combines Event Clock Automata (ECA) and Visibly Pushdown Automata (VPA). ECNA allow to express real-time properties over non-regular patterns of recursive programs. We prove that ECNA retain the closure and decidability properties of ECA and VPA being closed under Boolean operations and having a decidable language-inclusion problem. In particular, we prove that emptiness, universality, and language-inclusion for ECNA are Exptime-complete problems. As for the expressiveness, we have that ECNA properly extend any previous attempt in the literature of combining ECA and VPA.

2018

We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an integer sort. This subsumes analogous expressibility results previously known for finite and pushdown timed automata with untimed stack. As key technical tools, we use quantifier elimination for a fragment of hybrid linear arithmetic and for cyclic order atoms, and a reduction to register pushdown automata over cyclic order atoms.

Lecture Notes in Computer Science, 2006

We consider a general notion of timed automata with inputdetermined guards and show that they admit a robust logical framework along the lines of [6], in terms of a monadic second order logic characterisation and an expressively complete timed temporal logic. We then generalise these automata using the notion of recursive operators introduced by Henzinger, Raskin, and Schobbens [9], and show that they admit a similar logical framework. These results hold in the "pointwise" semantics. We finally use this framework to show that the real-time logic MITL of Alur et al [2] is expressively complete with respect to an MSO corresponding to an appropriate input-determined operator.

Lecture Notes in Computer Science

Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operations are driven by the input. In this paper, we consider VPA with two stacks, namely 2-VPA. These automata introduce a useful model to effectively describe concurrent pushdown systems using a simple communication mechanism between stacks. We show that 2-VPA are strictly more expressive than VPA. Indeed, 2-VPA accept some context-sensitive languages that are not context-free and some context-free languages that are not accepted by any VPA. Nevertheless, the class of languages accepted by 2-VPA is closed under all boolean operations and determinizable in ExpTime, but does not preserve decidability of emptiness problem. By adding an ordering constraint on stacks (2-OVPA), decidability of emptiness can be recovered (preserving desirable closure properties) and solved in PTime. Using these properties along with the automata-theoretic approach, we prove that the model checking problem over 2-OVPA models against 2-OVPA specifications is ExpTime-complete. Work partially supported by MIUR FIRB Project no. RBAU1P5SS.

Lecture Notes in Computer Science, 2005

We develop a structural and language theoretical characterization of timed languages over discrete time in terms of a variant of Büchi automata and languages. The so-called tick automaton is a standard Büchi automaton with a special "clock-tick"-input symbol modeling the discrete flow of time. Based on these characterizations we give an alternative proof for the fact that the class of regular timed languages is closed under complementation and formulate a time-warp lemma which, similar to a pumping lemma, can be used to show that a timed language is not regular. The characterizations hold alike for timed automata with and without periodic clock constraints.

Proceedings of the 4th International Conference on Automated Technology For Verification and Analysis, 2006

In previous work, the timed logic TCTL was extended with an "almost everywhere" Until modality which abstracts negligible sets of positions (i.e. with a null duration) along a run of a timed automaton. We propose here an extension of this logic with more powerful modalities, in order to specify properties abstracting transient states, which are events that last for less than k time units. Our main result is that modelchecking is still decidable and PSPACE-complete for this extension. On the other hand, a second semantics is defined, in which we consider the total duration where the property does not hold along a run. In this case, we prove that model-checking is undecidable. evolve at the rate of time (as in timed automata), are sometimes not expressive enough, hybrid variables (with multiple slopes) have been considered. The resulting model of hybrid automata has been largely studied in the subsequent years [16]. However, while some decidability results could be obtained [3, 18], using stopwatches (i.e. variables with slopes 0 and 1) already leads to undecidability for the reachability problem [2]. Further research has thus been devoted to weaker models where hybrid variables are only used as observers, i.e. are not tested in the automaton and thus play no role during a computation. These variables, sometimes called costs or prices in this context can be used in an optimization criterium [3, 7, 8, 11] or as constraints in temporal logic formulas. For instance, the logic WCTL [12, 10], interpreted over timed automata extended with costs, adds cost contraints on modalities: it is possible to express that a given state is reachable within a fixed cost bound. Abstracting transient states. When practical examples are considered, the need for abstracting transient states often happens. For example, modeling the instantaneous changes of a variable may introduce artificial (and thus non pertinent) transient states in the model. This motivated the work in [9], where configurations with zero duration could be abstracted by introducing into TCTL the almost everywhere U a modality. However, this is not sufficient in some cases. Contribution. In this paper, we propose an extension of TCTL called TCTL ∆ , which brings out a powerful generalization of the results in [9]. We introduce a new modality U k , where k ∈ N is a parameter, in order to abstract events that do not last continuously for at least k time units (t.u). For example, AF 2 ≤100 alarm expresses that for any execution, the atomic proposition alarm becomes true before 100 t.u and will hold for at least 2 time units. One also could express the fact that an event a precedes an event b along any run, an event being actually considered iff it lasts for at least k time units: the formula ArequestP 3 grant states that along any run where grant has occurred for a duration greater than 3, a request has been emitted continusously for a duration greater than 3. We prove that model-checking for TCTL ∆ is still PSPACE-complete. While the analogous result for TCTL or the extended version of [9] relies on the standard notion of equivalent runs, we have to define a stronger form for this equivalence, in order to obtain the consistency of TCTL ∆-formulae on the regions of the timed automaton. Finally, we also consider a global semantics, called TCTL ∆ Σ , for which the global duration during which a property does not hold, is bounded by a fixed constant k. Although this semantics is more natural and uses only observer hybrid variables in the model, we prove that model-checking TCTL ∆ Σ is undecidable. Outline. Section 2 recalls the main features of timed automata model and gives definitions for the syntax and semantics of our extended logics. Sections 3 and 4 are devoted to the model-checking of TCTL ∆ and, in the last section, we show that model-checking the extended logic TCTL ∆ Σ is undecidable.

ArXiv, 2018

We study the reachability problem for networks of timed communicating processes. Each process is a timed automaton communicating with other processes by exchanging messages over unbounded FIFO channels. Messages carry clocks which are checked at the time of transmission and reception with suitable timing constraints. Each automaton can only access its set of local clocks and message clocks of sent/received messages. Time is dense and all clocks evolve at the same rate. Our main contribution is a complete characterisation of decidable and undecidable communication topologies generalising and unifying previous work. From a technical point of view, we use quantifier elimination and a reduction to counter automata with registers.

Electronic Proceedings in Theoretical Computer Science, 2018

The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (EC NTL) and Nested Metric Temporal Logic (NMTL). The logic EC NTL is an extension of both the logic CaRet (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of EC NTL and visibly model-checking of Visibly Pushdown Timed Automata (VPTA) against EC NTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to EC NTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete. * The work by Adriano Peron and Aniello Murano has been partially supported by the GNCS project Formal methods for verification and synthesis of discrete and hybrid systems and by Dept. project MODAL MOdel-Driven Analysis of Critical Industrial Systems.

2009

A linear time extension of deterministic pushdown automata is introduced that recognizes all deterministic context-free languages, but also languages such as {a n b n c n | n ≥ 0} and the MIX language. It is argued that this new class of automata, called λ-acyclic read-first deterministic stack+bag pushdown automata, has applications in natural language processing. * Thanks to Thomas Hanneforth for pointing out previous work on φ-transitions to me.