Abstract
A number of algorithms for computing the simulation preorder on Kripke structures and on labelled transition systems are available. Among them, the algorithm by Ranzato and Tapparo [2007] has the best time complexity,while the algorithm by Gentilini et al. [2003] - successively corrected by van Glabbeek and Ploeger [2008] - has the best space complexity. Both space and time complexities are critical issues in a simulation algorithm, in particular memory requirements are crucial in the context of model checking when dealing with large state spaces. Here, we propose a new simulation algorithm that is obtained as a space saving modification of the time efficient algorithm by Ranzato and Tapparo: a symbolic representation of sets is embedded in this algorithm so that any set of states manipulated by the algorithm can be efficiently stored as a set of blocks of a suitable state partition. It turns out that this novel simulation algorithm has a space complexity comparable with Gentilini et al.'s algorithm while improving on Gentilini et al.'s time bound.
Highlights
Deciding whether a formal language contains another one is a fundamental problem with diverse applications ranging from automata-based verification to compiler construction [6, 13, 25, 42]
We introduce different well-quasiorders to be used in our inclusion algorithm and we show that using distinct well-quasiorder-based abstractions for prefixes and periods pays off
We start with the following research question: What is the impact in having separate qos for prefixes and periods? To answer it, we first examine the performance of BAIT on the contrived family of examples of Fig. 2
Summary
Deciding whether a formal language contains another one is a fundamental problem with diverse applications ranging from automata-based verification to compiler construction [6, 13, 25, 42]. We deal with the inclusion problem for ω-languages, namely languages of words of infinite length (ω-words) over a finite alphabet. We put forward a number of language inclusion algorithms that are systematically designed from an abstraction-based perspective of the inclusion problem. Our starting point was a recent abstract interpretation-based algorithmic framework for the inclusion problem for languages of finite words [15, 16]. Extending this framework to ω-words raises several challenges. The finite word case crucially relies on least fixpoint characterizations of languages which we are not aware of for languages of ω-words (while greatest fixpoint characterizations exist). The second challenge is to define suitable abstractions for languages of ω-words and effective representations thereof
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