Syntactic Complexity of Circular Semi-Flower Automata

TL;DR

This paper studies the syntactic complexity of specific automata models called circular semi-flower automata, revealing linear complexity for certain cases and a quadratic formula for others, advancing understanding of automata structure.

Contribution

It provides new formulas and bounds for the syntactic complexity of CSFA with different numbers of branch points, extending automata theory knowledge.

Findings

Linear syntactic complexity for CSFA with at most one bpi

Quadratic complexity formula for 2-bpi CSFA over binary alphabet

Explicit complexity bounds for specific automata configurations

Abstract

We investigate the syntactic complexity of certain types of finitely generated submonoids of a free monoid. In fact, we consider those submonoids which are accepted by circular semi-flower automata (CSFA). Here, we show that the syntactic complexity of CSFA with at most one `branch point going in' (bpi) is linear. Further, we prove that the syntactic complexity of $n$-state CSFA with two bpis over a binary alphabet is $2n(n+1)$.