By Morris Rubinoff, Marshall C. Yovits
Seeing that its first quantity in 1960, Advances in desktops has awarded certain insurance of techniques in and software program and in machine thought, layout, and purposes. It has additionally supplied participants with a medium within which they could study their matters in larger intensity and breadth than that allowed via usual magazine articles. for this reason, many articles became general references that stay of important, lasting worth regardless of the speedy progress happening within the box.
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Extra resources for Advances in Computers, Vol. 14
Math. Symp. Theor. Comput. pp. 66-71. Fagin, R. (1974). Generalized firsborder spectra and polynomial-time recognizable sets. fnd. Appl. -Amer. Math. )Proc. 7, 43-73. Fischer, M. , and Rabin, M. 0. (1974). Super-exponential complexity of Pressburger arithmetic. Ind. Appl. -Amer. Math. )Proc. 7, 2 7 4 1 . Garey, M. , Johnson, D. , and Stockmeyer, L. (1974). Some simplified NP-complete problems. Proc. 7th Annu. Ass. Comput. Mach. Symp. Theor. Comput. pp. 47-63. Greibach, 8. (1973). The hardest context-free language.
Now the way to generate the transition matrix in time O(nZk), where n is the length of the input, is (a) we generate all integers in the range 0 - (2nk - 1) and call these configurations c;. (b) As in the matrix product routine, we form ( c o ) (cl) . . ( ~ ~ - 1m,) where m = 2nk and (c;) means m-fold concatenation, and (cocl . . , obtain a vector of bits which is 1 iff c j follows from c i ) . This completes the description of our simulation algorithm: put,ting everything together we have a procedure which runs in polynomial time, since the matrix may be computed in 0 ( (log 2cnk) z, moves and its transitive closure in 0 ( (log 2enk)z, = 0 (nzk)moves.
Cornput. 2,304-310. , and Hopcroft, J. E. (1971). An overview of the theory of computational complexity. J . Ass. Comput. Mach. 18, 444-475. , and Hunt, H. , 111. (1974). The 1ba problem and its importance in the theory of computing. Ind. Appl. -Amer. Math. ) PTOC. 7, 1-26. , and Shank, H. (1968). On the recognition of primes by automata. J . Ass. Comput. Mach. 15, 382-389. , and Shank, H. (1969). Two memory bounds for the recognition of primes by automata. Math. Syst. Theory 3, 125-129. , and Simon, J.