Games Played on Finite Graphs
studying computations one can follow several approaches. One approach can generally be called a computational model approach. In this approach one defines the notion of a computational model, gives exact mathematical definition to the notion of computation, and then studies languages recognized by these models. for instance, this is what we did in the previous two chapters: we defined finite automata, Büchi automata, and computations on these machines and studied Languages recognized by these machines and their properties. Another approach can generally be called an algebraic approach. In this approach one identifies computational models with finite algebras and employs known algebraic results in order study computations. This is an example of a fruitful interaction of two distinct areas in which notions from the theory of computations interplay with the notions of algebra, and lead to new ideas and concepts. This approach is not in the scope of this book, and hence we will not discuss it.
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