Infinite trees and automaton-definable relations over &ohgr;-words
Theoretical Computer Science - Selected papers of the 7th Annual Symposium on theoretical aspects of computer science (STACS '90) Rouen, France, February 1990
Automata, Languages, and Machines
Automata, Languages, and Machines
Word Processing in Groups
Definable relations and first-order query languages over strings
Journal of the ACM (JACM)
Two-Variable Logic on Words with Data
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Model checking freeze LTL over one-counter automata
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
The "equal last letter" predicate for words on infinite alphabets and classes of multitape automata
Theoretical Computer Science
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Eilenberg, Elgot and Shepherdson showed in 1969, [S. Eilenberg, C.C. Elgot, J.C. Shepherdson, Sets recognized by n-tape automata, Journal of Algebra 13 (1969) 447-464], that a relation on finite words over a finite, non-unary alphabet with p letters is definable in first order logic with p+2 predicates for the relations equal length, prefix and last letter isa (for each letter a@?@S) if and only if it can be recognized by a finite multitape synchronous automaton, i.e., one whose read heads move simultaneously. They left open the characterization in the case of infinite alphabets, and proposed some conjectures concerning them. We solve all problems and sharpen the main theorem of [S. Eilenberg, C.C. Elgot, J.C. Shepherdson, Sets recognized by n-tape automata, Journal of Algebra 13 (1969) 447-464].