Abstract:
This paper is a review of several results that connect the areas of theoretical computer science (particularly automata theory and context-free grammars) and logic (particularly decidability results of the second order theories). In particular, the properties of the set of trees accepted by finite state tree acceptors- also called recognizable sets are studied. The results presented are interesting because they give rise to an alternate characterization of the notion of a context-free grammar resulting in a descriptive complexity result for the theory of context-free languages and on the other hand, the results presented give a novel decidability result for the theory of n successor functions, the novelty lying in the use of tools from automata theory for the proof. And so, while this paper looks at applications of automata over trees and other objects to fields such as logic and context free grammars, the objective is to highlight how looking at these question through this way brings together notions from seemingly disparate fields. The focus will be to explicate these results to show how recognizable sets can be viewed as useful both to the theory of context free grammars
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