Programs Versus Finite Tree-Programs

TL;DR

This paper investigates the equivalence between general programs with cycles and finite tree-programs for certain classes of structures, extending results to programs similar to computation trees.

Contribution

It establishes conditions under which programs with cycles are equivalent to finite tree-programs for specific structures, advancing understanding of program structure and computation models.

Findings

Programs with cycles are equivalent to finite tree-programs for certain classes of structures.

Extends results to programs resembling computation trees, showing equivalence in those cases.

Provides theoretical foundations for understanding the relationship between general programs and tree-based programs.

Abstract

In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most countably many nodes. We start with programs in which arbitrary terms of a given signature may be used in function nodes and arbitrary formulas of this signature may be used in predicate nodes. We then extend our results to programs that are close in nature to computation trees: if such a program is a finite tree-program, then it is an ordinary computation tree.