Faculty of Computing and Information Science >
Computing and Information Science >
Computing and Information Science Technical Reports >
Please use this identifier to cite or link to this item:
|Title: ||Halting and Equivalence of Program Schemes in Models of Arbitrary Theories|
|Authors: ||Kozen, Dexter|
|Keywords: ||dynamic model theory|
|Issue Date: ||19-May-2010|
|Abstract: ||In this note we consider the following decision problems. Let S be a fixed first-order signature.
(i) Given a first-order theory or ground theory T over S of Turing degree A, a program scheme p over S, and input values specified by ground terms t1,...,tn, does p halt on input t1,...,tn in all models of T?
(ii) Given a first-order theory or ground theory T over S of Turing degree A and two program schemes p and q over S, are p and q equivalent in all models of T?
When T is empty, these two problems are the classical halting and equivalence problems for program schemes, respectively. We show that problem (i) is Sigma^A_1-complete and problem (ii) is Pi^A_2-complete. Both problems remain hard for their respective complexity classes even if S is restricted to contain only a single constant, a single unary function symbol, and a single monadic predicate. It follows from (ii) that there can exist no relatively complete deductive system for scheme equivalence over models of theories of any Turing degree.|
|Appears in Collections:||Computing and Information Science Technical Reports|
Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.