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- Wolfgang Thomas
- 1996

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)

Innnite two-person games are a natural framework for the study of reactive nonterminating programs. The eeective construction of winning strategies in such games is an approach to the synthesis of reactive programs. We describe the automata theoretic setting of innnite games (given by \game graphs"), outline a new construction of winning strategies in… (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)

The monadic second-order quantiier alternation hierarchy over the class of nite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely nite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the diierence between the… (More)