Finite Automata, Formal Logic, and Circuit Complexity
[Book]
by Howard Straubing.
Boston, MA
Birkhäuser Boston : Imprint : Birkhäuser
1994
(xii, 227 pages)
Progress in theoretical computer science.
I Mathematical Preliminaries --;I.1 Words and Languages --;I.2 Automata and Regular Languages --;I.3 Semigroups and Homomorphisms --;II Formal Languages and Formal Logic --;II. 1 Examples --;II. 2 Definitions --;III Finite Automata --;III. 1 Monadic Second-Order Sentences and Regular Languages --;III. 2 Regular Numerical Predicates --;III. 3 Infinite Words and Decidable Theories --;IV Model-Theoretic Games --;IV. 1 The Ehrenfeucht-Fraïssé Game --;IV. 2 Application to FO].
One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup- theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger.