Universality and semicomputability for nondeterministic programming languages over abstract algebras

tract Algebras Wei Jiang∗ , Yuan Wang† , and Jeffery Zucker‡ September 11, 2006 The Universal Function Theorem (UFT) originated in 1930s with the work of Alan Turing, who proved the existence of a universal Turing machine for computations on strings over a finite alphabet. This stimulated the development of stored-program computers. Classical computability theory, including the UFT and the theory of semicomputable sets, has been extended by Tucker and Zucker to abstract manysorted algebras, with algorithms formalized as deterministic While programs. This paper investigates the extension of this work to the nondeterministic programming languages WhileRA consisting of While programs extended by random assignments, as well as sublanguages of WhileRA formed by restricting the random assignments to booleans or naturals only. It also investigates the nondeterministic language GC of guarded commands. There are two topnvestigation: (1) the extent to which the UFT holds over abstract a...

• Type: Journal
• Year: 2007
• Where: JLP
• Authors: Wei Jiang, Yuan Wang, Jeffery I. Zucker
• Keywords: Algebras Wei Jiang∗, Jeffery Zucker‡ September, JLP 2007, Random Assignments