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The Equality Problem for Rational Series With Multiplicities in the Tropical Semiring is Undecidable
, 1994
"... this paper that the equality problem for Mrational series over an alphabet with at least two letters is undecidable. ..."
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Cited by 54 (2 self)
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this paper that the equality problem for Mrational series over an alphabet with at least two letters is undecidable.
Message Sequence Graphs and Decision Problems on Mazurkiewicz Traces
 In Proc. of MFCS'99, LNCS 1672
, 1999
"... Message sequence charts (MSC) are a graphical specification language widely used for designing communication protocols. Our starting point are two decision problems concerning the correctness and the consistency of a design based by MSC graphs. Both problems are shown to be undecidable, in gener ..."
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Cited by 44 (11 self)
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Message sequence charts (MSC) are a graphical specification language widely used for designing communication protocols. Our starting point are two decision problems concerning the correctness and the consistency of a design based by MSC graphs. Both problems are shown to be undecidable, in general. Using a natural connectivity assumption from Mazurkiewicz trace theory we show both problems to be EXPSPACEcomplete for locally synchronized graphs. The results are based on new complexity results for starconnected rational trace languages.
Recognizable Sets with Multiplicities in the Tropical Semiring
, 1988
"... The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the MinPlus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's ..."
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Cited by 32 (1 self)
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The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the MinPlus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's classical star height problem and the measure of the nondeterministic complexity of finite automata. We review here these results, their applications and point out some open problems. 1 Introduction One of the richest extensions of finite automaton theory is obtained by associating multiplicities to words, edges and states. Perhaps the most intuitive appearence of this concept is obtained by counting for every word the number of successful paths spelling it in a (nondeterministic) finite automaton. This is motivated by the formalization of ambiguity in a finite automaton and leads to the theory of recognizable subsets of a free monoid with multiplicities in the semiring of natural numbers. This...
Kleene algebra with tests: Completeness and decidability
 In Proc. of 10th International Workshop on Computer Science Logic (CSL’96
, 1996
"... Abstract. Kleene algebras with tests provide a rigorous framework for equational speci cation and veri cation. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene alg ..."
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Cited by 26 (10 self)
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Abstract. Kleene algebras with tests provide a rigorous framework for equational speci cation and veri cation. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra with tests and *continuous Kleene algebra with tests over languagetheoretic and relational models. We also show decidability. Cohen's reduction of Kleene algebra with hypotheses of the form r = 0 to Kleene algebra without hypotheses is simpli ed and extended to handle Kleene algebras with tests. 1
On the Complexity of Reasoning in Kleene Algebra
 Information and Computation
, 1997
"... We study the complexity of reasoning in Kleene algebra and *continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E ! s = t, where E is a finite set of equations. We obtain various levels of complexi ..."
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Cited by 10 (4 self)
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We study the complexity of reasoning in Kleene algebra and *continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E ! s = t, where E is a finite set of equations. We obtain various levels of complexity based on the form of the assumptions E. Our main results are: for * continuous Kleene algebra, ffl if E contains only commutativity assumptions pq = qp, the problem is \Pi 0 1 complete; ffl if E contains only monoid equations, the problem is \Pi 0 2 complete; ffl for arbitrary equations E, the problem is \Pi 1 1  complete. The last problem is the universal Horn theory of the *continuous Kleene algebras. This resolves an open question of Kozen (1994). 1 Introduction Kleene algebra (KA) is fundamental and ubiquitous in computer science. Since its invention by Kleene in 1956, it has arisen in various forms in program logic and semantics [17, 28], relational algebra [27, 32], aut...