On the toggling-branching recurrence of Computability Logic

TL;DR

This paper introduces a simplified version of the toggling-branching recurrence in Computability Logic, proves its equivalence to the original, and shows both preserve the static property of their arguments.

Contribution

A new simplified toggling-branching recurrence operation is proposed, demonstrating equivalence to the canonical version and preservation of static properties.

Findings

Simplified toggling-branching recurrence is equivalent to the original.

Both versions preserve the static property of arguments.

The new operation maintains key properties of Computability Logic.

Abstract

We introduce a new, substantially simplified version of the toggling-branching recurrence operation of Computability Logic, prove its equivalence to Japaridze's old, "canonical" version, and also prove that both versions preserve the static property of their arguments.