State Complexity of Catenation Combined with Star and Reversal
Bo Cui (The University of Western Ontario), Yuan Gao (The University, of Western Ontario), Lila Kari (The University of Western Ontario), Sheng Yu, (The University of Western Ontario)
TL;DR
This paper investigates the state complexity of combined operations involving catenation with star and reversal, revealing that their complexities are significantly lower than expected from individual operation complexities.
Contribution
It provides new bounds on the state complexity of combined catenation with star and reversal operations, improving understanding of their computational properties.
Findings
State complexities are lower than the product of individual complexities.
Derived bounds for combined catenation with star and reversal.
Implications for automata minimization and language processing.
Abstract
This paper is a continuation of our research work on state complexity of combined operations. Motivated by applications, we study the state complexities of two particular combined operations: catenation combined with star and catenation combined with reversal. We show that the state complexities of both of these combined operations are considerably less than the compositions of the state complexities of their individual participating operations.
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