Easy multiplications. I. The realm of Kleene's theorem
Information and Computation
On the valuedness of finite transducers
Acta Informatica
Theoretical Computer Science
Word Processing in Groups
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Automatic linear orders and trees
ACM Transactions on Computational Logic (TOCL)
On the Problem Whether the Image of an N-Rational Series Equals
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
The Isomorphism Problem on Classes of Automatic Structures
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Singular artin monoids of finite coxeter type are automatic
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Invariants of automatic presentations and semi-synchronous transductions
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Automatic presentations for finitely generated groups
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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In this paper, we report on applications of weighted automata in the theory of automatic structures. All (except one) result were known before, but their proof using weighted automata is novel. More precisely, we prove that the extension of first-order logic by the infinity ∃∞, the modulo ∃(p,q), and the (new) boundedness quantifier is decidable. The first two quantifiers are handled using closure properties of the class of recognizable formal power series and the fact that the preimage of a value under a recognizable formal power series is regular if the semiring is finite. Our reasoning regarding the boundedness quantifier uses Weber's decidability result of finite-valued rational transductions. We also show that the isomorphism problem of automatic structures is undecidable using an undecidability result on recognizable formal power series due to Honkala.