Abstract: In the disclosed position-deterministic machine (PDM) and its simulation methods, a user problem to be solved is represented as a special kind of nondeterministic Turing machine, called PDM, with an input X to it. Deterministic methods of using deterministic components and recursive relations for the simulation of a PDA on an input X are disclosed. The disclosed methods decrease deterministic computational time complexity from 2T(n) currently to nT(n) in the present invention for a PDM of nondeterministic computational time complexity T(n) on an input X of length n.

Abstract: In the disclosed nondeterministic computing apparatus and methods, a user problem to be solved is represented as a nondeterministic Turing machine M with an input X to it. A method for deterministic simulation of M on X is disclosed, which performs assumptions and refutations. The disclosed method is the first deterministic method with polynomial time complexity in the worst case if the time complexity of M is of polynomial time complexity, where time complexity is measured as a function of the length of X.

Abstract: In the disclosed nondeterministic computing apparatus, a user problem to be solved is translated into an equivalent system of clause polynomial equations (CPEQS) in GF(2). A process for finding an inconsistency in CPEQS is disclosed, which performs elementary equation (or row) operations, such as Gaussian forward eliminations, for each variable v in CPEQS by treating different monomials as different single variables in v-order. The result is examined for two kinds of equations: an inconsistent equation 1=0 and an equation which left-hand side has constant monomial 1 and v occurs in all the other monomials such that v occurs at least once while its right-hand side is 0 to find v=1. To find v=0, a substitution of v with v?1 is performed on CPEQS in advance. If either 1=0, or, x=1 and x=0 simultaneously for some variable x in CPEQS, then CPEQS is inconsistent; otherwise CPEQS is consistent.

Abstract: The present invention relates to a method for program transformation and an apparatus for COBOL to Java program transformation. The method consists of: (1) a new approach for statement-to-statement program transformation, facilitated by a predefined target language library, which keeps original comments, program control flow, functionality, and time complexity; (2) a new approach for goto statement elimination, which uses existing exception handling mechanism in target language and its implementation is hidden in a super class in a library; (3) a new extended BNF to distinguish different occurrences of the same term in a BNF production; (4) a new approach for embedded statement as a special marker statement and a comment, (5) in the description of the above, a program transformation specification language is defined to describe relationship between comments in two languages.