Two-Variable Ehrenfeucht-Fraisse Games over Omega-Terms

TL;DR

This paper explores the use of Ehrenfeucht-Fraisse games over omega-terms to characterize fragments of first-order logic on words, introducing simplified methods for two-variable logic using linear orders.

Contribution

It demonstrates that for two-variable logic, simpler linear orders suffice in Ehrenfeucht-Fraisse games to verify identities of omega-terms, improving previous approaches.

Findings

Simplified Ehrenfeucht-Fraisse games for two-variable logic

Use of linear orders in omega-term identities

Enhanced methods for logical fragment characterization

Abstract

Fragments of first-order logic over words can often be characterized in terms of finite monoids, and identities of omega-terms are an effective mechanism for specifying classes of monoids. Huschenbett and the first author have shown how to use infinite Ehrenfeucht-Fraisse games on linear orders for showing that some given fragment satisfies an identity of omega-terms (STACS 2014). After revisiting this result, we show that for two-variable logic one can use simpler linear orders.