Rational series and their languages
Rational series and their languages
Fractals everywhere
Real algebraic number computation using interval arithmetic
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Finite Automata Computing Real Functions
SIAM Journal on Computing
Undecidability in integer weighted finite automata
Fundamenta Informaticae - Special issue dedicated to A. Salomaa
Automata, Languages, and Machines
Automata, Languages, and Machines
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
Languages Accepted by Integer Weighted Finite Automata
Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa
On Computational Power of Weighted Finite Automata
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Decidable and Undecidable Problems in Matrix Theory
Decidable and Undecidable Problems in Matrix Theory
Bounding Recursive Procedural Models Using Convex Optimization
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Simpler and more general minimization for weighted finite-state automata
NAACL '03 Proceedings of the 2003 Conference of the North American Chapter of the Association for Computational Linguistics on Human Language Technology - Volume 1
Observations on the Smoothness Properties of Real Functions Computed by Weighted Finite Automata
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
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Parametric weighted finite automata (PWFA) are a multidimensional variant of weighted finite automata (WFA). In contrast to WFA, one primarily considers the set of vectors computed by a PWFA and not the function it computes. In this paper we show that the membership, emptiness and equivalence problems for PWFA are recursively undecidable and that there is no algorithm that effectively minimizes a PWFA. We study the correlation between iterated function systems (IFS) and the class cPWFA of PWFA that are based on contraction mappings, where we show that it is decidable, if a PWFA belongs to cPWFA, that automata in cPWFA compute affine transformations of the attractors of certain IFS, that the set of sets computable by automata in cPWFA is effectively closed under arbitrary affine transformation and that any PWFA computing a non compact set cannot be a member of cPWFA. For PWFA with unary alphabet we proof that the set of sets computable is effectively closed under set union and that the membership problem for unary alphabet integer PWFA is decidable.