Computations by fly-automata beyond monadic second-order logic

TL;DR

This paper introduces fly-automata, a flexible automata framework that extends beyond monadic second-order logic to efficiently compute graph properties related to tree-width and clique-width.

Contribution

It provides a new automata-based methodology for constructing dynamic programming algorithms that handle properties not expressible in monadic second-order logic.

Findings

Fly-automata can handle properties with infinite states due to counters.

The framework simplifies the construction of XP and FPT algorithms for graph problems.

Tools are provided for combining automata to build complex property-checking algorithms.

Abstract

We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not monadic second-order expressible because their states may include counters, so that their sets of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. Rather than new algorithmic results we present tools for constructing easily certain dynamic programming algorithms by combining predefined automata for basic functions and properties.