Advances in Computers, Vol. 14 by Morris Rubinoff, Marshall C. Yovits

By Morris Rubinoff, Marshall C. Yovits

Because its first quantity in 1960, Advances in pcs has provided targeted insurance of strategies in and software program and in desktop concept, layout, and purposes. It has additionally supplied individuals with a medium within which they could study their matters in better intensity and breadth than that allowed via ordinary magazine articles. for that reason, many articles became commonplace references that stay of vital, lasting price regardless of the quick development happening within the box.

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5th Annu. Ass. Comput. Mach. Symp. Theor. Comput. pp. 1-9. , and Stockmeyer, L. (1975). “Inherent Computational Complexity of Decision Problems in Logic and Automata Theory,” Lecture Notes in Computer Science. Springer-Verlag, Berlin and New York. Miller, G. L. (1975). Riemann’s hypotheses and tests of primality. Proc. ‘7thAnnu. Ass. Comput. Mach. Symp. Theor. Comput. pp. 234-239. Minsky, M. (1970). Form and content in computer science. J . Ass. Comput. Mach. 17, 197-215. Myhill, J. (1960). Linearly bounded automata.

Contr. 3, 207-223. Landweber, P. S. (1963). Three theorems on phrase structure grammars of type 1. Inform. Contr. 2 , 131-136. , and Yamada, H. (1964). Regular expressions and state graphs. In “Sequential Machines: Selected Papers” (E. F. ), pp. 157-175. Addison-Wesley, Reading, Massachusetts. Meyer, A. (1973). “Weak Monadic Second Order Theory of Successor Is Not Elementary Recursive,” Proj. MAC T M 38. Massachusetts Institute of Technology, Cambridge. , and Stockmeyer, L. (1972). The equivalence problem for regular expressions with squaring requires exponential space.

As long as we must describe the T m computations explicitly, the equivalence problem will be soluble, and its computational difficulty depends on the descriptive power of the formalism. Some of the most interesting applications of this principle have yielded the computational complexity of decision procedures for decidable logical theories. The results are rather depressing in that even for apparently simple theories the decision complexity makes them practically undecidable. We cite two such results.

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