683 research outputs found
A Unifying Approach to Decide Relations for Timed Automata and their Game Characterization
In this paper we present a unifying approach for deciding various
bisimulations, simulation equivalences and preorders between two timed automata
states. We propose a zone based method for deciding these relations in which we
eliminate an explicit product construction of the region graphs or the zone
graphs as in the classical methods. Our method is also generic and can be used
to decide several timed relations. We also present a game characterization for
these timed relations and show that the game hierarchy reflects the hierarchy
of the timed relations. One can obtain an infinite game hierarchy and thus the
game characterization further indicates the possibility of defining new timed
relations which have not been studied yet. The game characterization also helps
us to come up with a formula which encodes the separation between two states
that are not timed bisimilar. Such distinguishing formulae can also be
generated for many relations other than timed bisimilarity.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690
Deterministic Timed Finite State Machines: Equivalence Checking and Expressive Power
There has been a growing interest in defining models of automata enriched
with time. For instance, timed automata were introduced as automata extended
with clocks. In this paper, we study models of timed finite state machines
(TFSMs), i.e., FSMs enriched with time, which accept timed input words and
generate timed output words. Here we discuss some models of TFSMs with a single
clock: TFSMs with timed guards, TFSMs with timeouts, and TFSMs with both timed
guards and timeouts. We solve the problem of equivalence checking for all three
models, and we compare their expressive power, characterizing subclasses of
TFSMs with timed guards and of TFSMs with timeouts that are equivalent to each
other.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Process algebra for performance evaluation
This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions
Expected-Delay-Summing Weak Bisimilarity for Markov Automata
A new weak bisimulation semantics is defined for Markov automata that, in
addition to abstracting from internal actions, sums up the expected values of
consecutive exponentially distributed delays possibly intertwined with internal
actions. The resulting equivalence is shown to be a congruence with respect to
parallel composition for Markov automata. Moreover, it turns out to be
comparable with weak bisimilarity for timed labeled transition systems, thus
constituting a step towards reconciling the semantics for stochastic time and
deterministic time.Comment: In Proceedings QAPL 2015, arXiv:1509.0816
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically
Labeled state-to-function transition systems, FuTS for short, are
characterized by transitions which relate states to functions of states over
general semirings, equipped with a rich set of higher-order operators. As such,
FuTS constitute a convenient modeling instrument to deal with process languages
and their quantitative extensions in particular. In this paper, the notion of
bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A
correspondence result is established stating that FuTS-bisimilarity coincides
with behavioural equivalence of the associated functor. As generic examples,
the equivalences underlying substantial fragments of major examples of
quantitative process algebras are related to the bisimilarity of specific FuTS.
The examples range from a stochastic process language, PEPA, to a language for
Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a
language for Markov Automata, MAL. The equivalences underlying these languages
are related to the bisimilarity of their specific FuTS. By the correspondence
result coalgebraic justification of the equivalences of these calculi is
obtained. The specific selection of languages, besides covering a large variety
of process interaction models and modelling choices involving quantities,
allows us to show different classes of FuTS, namely so-called simple FuTS,
combined FuTS, nested FuTS, and general FuTS
Behavioural equivalences for timed systems
Timed transition systems are behavioural models that include an explicit
treatment of time flow and are used to formalise the semantics of several
foundational process calculi and automata. Despite their relevance, a general
mathematical characterisation of timed transition systems and their behavioural
theory is still missing. We introduce the first uniform framework for timed
behavioural models that encompasses known behavioural equivalences such as
timed bisimulations, timed language equivalences as well as their weak and
time-abstract counterparts. All these notions of equivalences are naturally
organised by their discriminating power in a spectrum. We prove that this
result does not depend on the type of the systems under scrutiny: it holds for
any generalisation of timed transition system. We instantiate our framework to
timed transition systems and their quantitative extensions such as timed
probabilistic systems
O-Minimal Hybrid Reachability Games
In this paper, we consider reachability games over general hybrid systems,
and distinguish between two possible observation frameworks for those games:
either the precise dynamics of the system is seen by the players (this is the
perfect observation framework), or only the starting point and the delays are
known by the players (this is the partial observation framework). In the first
more classical framework, we show that time-abstract bisimulation is not
adequate for solving this problem, although it is sufficient in the case of
timed automata . That is why we consider an other equivalence, namely the
suffix equivalence based on the encoding of trajectories through words. We show
that this suffix equivalence is in general a correct abstraction for games. We
apply this result to o-minimal hybrid systems, and get decidability and
computability results in this framework. For the second framework which assumes
a partial observation of the dynamics of the system, we propose another
abstraction, called the superword encoding, which is suitable to solve the
games under that assumption. In that framework, we also provide decidability
and computability results
Modelling MAC-Layer Communications in Wireless Systems
We present a timed process calculus for modelling wireless networks in which
individual stations broadcast and receive messages; moreover the broadcasts are
subject to collisions. Based on a reduction semantics for the calculus we
define a contextual equivalence to compare the external behaviour of such
wireless networks. Further, we construct an extensional LTS (labelled
transition system) which models the activities of stations that can be directly
observed by the external environment. Standard bisimulations in this LTS
provide a sound proof method for proving systems contextually equivalence. We
illustrate the usefulness of the proof methodology by a series of examples.
Finally we show that this proof method is also complete, for a large class of
systems
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