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This paper gives a personal account of some developments in automata theory and computational complexity theory. Though the account is subjective and deals primarily with the research areas of direct interest to the author, it discusses the underlying beliefs and philosophy which guided this research as well as the intellectual environment and the ideas and contacts which influenced it. An attempt...
Straight line programs in which array elements can be referenced and set are considered. Two programs are equivalent if they compute the same expression as a function of the inputs. Testing the equivalence of programs with arrays is shown to be NP-complete, while programs without arrays can be tested for equivalence in linear time. Equivalence testing takes polynomial time when programs have either...
The s-languages are those languages recognized by a particular restricted form of deterministic pushdown automaton, called an s-machine. They are uniquely characterized by that subset of the standard-form grammars in which each rule has the form Z → aY1...Yn, n≥0, and for which the pairs (Z, a) are distinct among the rules. It is shown that the s-languages have the prefix property, and that they include...
In this paper we investigate how numbers, functions, and sequences can be classified according to their computational complexity. The computational complexity is measured by how fast the number or function can be computed by a multitape computer (Turing machine). It is shown that by means of this measure the computational complexity of numbers and functions can be submitted to rigorous mathematical...
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