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Roadmap of Infinite Results
, 2008
"... This paper provides a comprehensive summary of equivalence checking results for infinitestate systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the webpage ..."
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This paper provides a comprehensive summary of equivalence checking results for infinitestate systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the webpage
Resumptions, Weak Bisimilarity and BigStep Semantics for While with Interactive I/O: An Exercise in Mixed InductionCoinduction
"... We look at the operational semantics of languages with interactive I/O through the glasses of constructive type theory. Following on from our earlier work on coinductive tracebased semantics for While [17], we define several bigstep semantics for While with interactive I/O, based on resumptions an ..."
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We look at the operational semantics of languages with interactive I/O through the glasses of constructive type theory. Following on from our earlier work on coinductive tracebased semantics for While [17], we define several bigstep semantics for While with interactive I/O, based on resumptions and terminationsensitive weak bisimilarity. These require nesting inductive definitions in coinductive definitions, which is interesting both mathematically and from the pointofview of implementation in a proof assistant. After first defining a basic semantics of statements in terms of resumptions with explicit internal actions (delays), we introduce a semantics in terms of delayfree resumptions that essentially removes finite sequences of delays on the fly from those resumptions that are responsive. Finally, we also look at a semantics in terms of delayfree resumptions supplemented with a silent divergence option. This semantics hinges on decisions between convergence and divergence and is only equivalent to the basic one classically. We have fully formalized our development in Coq. 1
The Complexity of BisimilarityChecking for OneCounter Processes
"... We study the problem of bisimilaritychecking between processes of onecounter automata and finitestate processes. We show that deciding weak bisimilarity between processes of onecounter nets (which are ‘restricted ’ onecounter automata where the counter cannot be tested for zero) and finitestat ..."
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We study the problem of bisimilaritychecking between processes of onecounter automata and finitestate processes. We show that deciding weak bisimilarity between processes of onecounter nets (which are ‘restricted ’ onecounter automata where the counter cannot be tested for zero) and finitestate processes is DPhard. In particular, this means that the problem is both NP and coNP hard. The same technique is used to demonstrate coNPhardness of strong bisimilarity between processes of onecounter nets. Then we design an algorithm which decides weak bisimilarity between processes of onecounter automata and finitestate processes in time which is polynomial for a large subclass of instances, giving a kind of characterization of all hard instances as a byproduct. Moreover, we show how to efficiently estimate the time which is needed to solve a given instance. Finally, we prove that the problem of strong bisimilarity between processes of onecounter automata and finitestate processes is in P.