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This paper is a survey on logical aspects of nite automata. Central points are the connection between nite automata and monadic second-order logic, the Ehrenfeucht-Fra ss e technique in the context of formal language theory, nite automata on !-words and their determinization, and a self-contained proof of the \Rabin Tree Theorem". Sections 5 and 6 contain(More)
Completeness and Weak Completeness Under Polynomial-Size Circuits p. 26 Communication Complexity of Key Agreement on Small Ranges p. 38 Pseudorandom Generators and the Frequency of Simplicity p. 50 Classes of Bounded Counting Type and their Inclusion Relations p. 60 Lower Bounds for Depth-Three Circuits With Equals and Mod-Gates p. 71 On Realizing Iterated(More)
When Ehrenfeucht introduced his game theoretic characterization of elementary equivalence in 1961, the rst application of these \Ehrenfeucht games" was to show that certain ordinals (considered as orderings) are indistinguishable in rst-order logic and weak monadic second-order logic. Here we review Shelah's extension of the method, the \composition of(More)