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Desert automata and the finite substitution problem
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A new model of weighted automata is introduced and the decidability of its limitedness problem is shown by solving the underlying Burnside problem.Abstract:
We give a positive solution to the so-called finite substitution problem which was open for more than 10 years [11]: given recognizable languages K and L, decide whether there exists a finite substitution σ such that σ(K) = L. For this, we introduce a new model of weighted automata and show the decidability of its limitedness problem by solving the underlying Burnside problem.read more
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Distance desert automata and the star height problem
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Regular Cost Functions over Finite Trees
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Regular Cost Functions, Part I: Logic and Algebra over Words
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Infinite-state games with finitary conditions
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Regular temporal cost functions
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References
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Journal ArticleDOI
The equality problem for rational series with multiplicities in the tropical semiring is undecidable
TL;DR: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not.
Journal ArticleDOI
Limitedness theorem on finite automata with distance functions
TL;DR: There exists an algorithm for deciding whether or not an arbitrary finite automaton with a distance function is limited in distance, and it is shown that this paper shows that this algorithm is available.
Proceedings ArticleDOI
Limited subsets of a free monoid
TL;DR: It follows that A is limited iff the infinite union in (1) can be replaced by the finiteunion in (2) for some m, and A islimited iff any concatenation of a finite number of elements of A can also be obtained by the concatenations of at most m elements of C.
Journal ArticleDOI
On semigroups of matrices over the tropical semiring
TL;DR: Factorization forests are used to prove finiteness results related to semigroups of matrices over M to recover results of Hashiguchi, Leung and the author in a unified combinatorial framework.