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 desktops has offered specified insurance of strategies in and software program and in computing device concept, layout, and purposes. It has additionally supplied participants with a medium within which they could research their topics in higher intensity and breadth than that allowed through ordinary magazine articles. consequently, many articles became general references that stay of vital, lasting price regardless of the fast development occurring within the box.

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Wc also need to gencrate up to I pairs of bits, multiply thcm in pairs, and add them up. This may be done as follows: we store the addresses of the two bits being computed, compute each of the two bits of the product scparatcly, multiply the two results and update the addresses to get the addrcsses of the two bits of the next product. The product is added to an accumulator and the process is repeated until all product terms have been computed. Then we need the carry from thc previous column. We cannot compute this carry by a recursive call of FIND, because since the length of the register may be exponential, keeping track of the recursion would take exponential tape.

The problem of recognizing the set of true sentences for the first-order propositional calculus (1EQ) is complete in P T A P E . 7: Proof: See Meyer and Stockmeyer (1973). Again we see that the difference in complexity between these two decision problems is directly related to the difference, if any, between N P and P TAPE. Next we take a look at how the computational complexity of the decision problem for regular expressions changes as we permit further operations. We know that all regular sets can be described by regular expressions using the operators u, -, *.

A string x E {O, 1) * is accepted by the RAM if there is a finite computation ending with the execution of an accept instruction. 32 J. HARTMANIS AND J . SIMON The complcxity measures definchd for R A M’s arr : (Unit) time measure: the complexity of an accepting computation is the number of instructions executed in the accepting sequcncc. The complexity of thc R A M on input z is the minimal complcxity of accepting computations. Logarzthmic, or length tame measure: the complexity of an accepting computation is the sum of the lengths of thc operands of the instructions executed in the accepting sequence.

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