22 research outputs found
Bisimulations over DLTS in O(m.log n)-time
The well known Hopcroft's algorithm to minimize deterministic complete
automata runs in -time, where is the size of the alphabet and
the number of states. The main part of this algorithm corresponds to the
computation of a coarsest bisimulation over a finite Deterministic Labelled
Transition System (DLTS). By applying techniques we have developed in the case
of simulations, we design a new algorithm which computes the coarsest
bisimulation over a finite DLTS in -time and -space, with
the number of transitions. The underlying DLTS does not need to be complete
and thus: . This new algorithm is much simpler than the two others
found in the literature.Comment: Submitted to DLT'1
Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking
The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade.\ud
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An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states.\ud
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To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced.\ud
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To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies
Scalable Minimization Algorithm for Partial Bisimulation
We present an efficient algorithm for computing the partial bisimulation
preorder and equivalence for labeled transitions systems. The partial
bisimulation preorder lies between simulation and bisimulation, as only a part
of the set of actions is bisimulated, whereas the rest of the actions are
simulated. Computing quotients for simulation equivalence is more expensive
than for bisimulation equivalence, as for simulation one has to account for the
so-called little brothers, which represent classes of states that can simulate
other classes. It is known that in the absence of little brother states,
(partial bi)simulation and bisimulation coincide, but still the complexity of
existing minimization algorithms for simulation and bisimulation does not
scale. Therefore, we developed a minimization algorithm and an accompanying
tool that scales with respect to the bisimulated action subset.Comment: In Proceedings WS-FMDS 2012, arXiv:1207.184
Conflict-preserving abstraction of discrete event systems using annotated automata
This paper proposes to enhance compositional verification of the nonblocking property of discrete event systems by introducing annotated automata. Annotations store nondeterministic branching information, which would otherwise be stored in extra states and transitions. This succinct representation makes it easier to simplify automata and enables new efficientmeans of abstraction, reducing the size of automata to be composed and thus the size of the synchronous product state space encountered in verification. The abstractions proposed are of polynomial complexity, and they have been successfully applied to model check the nonblocking property of the same set of large-scale industrial examples as used in related work
A State Minimization Algorithm for Communicating State Machines With Arbitrary Data Space
A fundamental issue in the automated analysis of communicating systems is the efficient generation of the reachable state space. Since it is not possible to generate all the reachable states of a system with an infinite number of states, we need a way to combine sets of states. In this paper, we describe communicating state machines with data variables, which we use to specify concurrent systems. We then present an algorithm that constructs the minimal reachability graph of a labeled transition system with infinite data values. Our algorithm clusters a set of states that are bisimilar into an equivalent class. We include an example to illustrate our algorithm and identify a set of sufficient conditions that guarantees the termination of the algorithm
Efficient Minimization of DFAs with Partial Transition Functions
Let PT-DFA mean a deterministic finite automaton whose transition relation is
a partial function. We present an algorithm for minimizing a PT-DFA in time and memory, where is the number of states, is
the number of defined transitions, and is the size of the alphabet.
Time consumption does not depend on , because the term arises
from an array that is accessed at random and never initialized. It is not
needed, if transitions are in a suitable order in the input. The algorithm uses
two instances of an array-based data structure for maintaining a refinable
partition. Its operations are all amortized constant time. One instance
represents the classical blocks and the other a partition of transitions. Our
measurements demonstrate the speed advantage of our algorithm on PT-DFAs over
an time, memory algorithm
Comparing Asynchronous -Complete Approximations and Quotient Based Abstractions
This paper is concerned with a detailed comparison of two different
abstraction techniques for the construction of finite state symbolic models for
controller synthesis of hybrid systems. Namely, we compare quotient based
abstractions (QBA), with different realizations of strongest (asynchronous)
-complete approximations (SAlCA) Even though the idea behind their
construction is very similar, we show that they are generally incomparable both
in terms of behavioral inclusion and similarity relations. We therefore derive
necessary and sufficient conditions for QBA to coincide with particular
realizations of SAlCA. Depending on the original system, either QBA or SAlCA
can be a tighter abstraction