Transition Complexity of Incomplete DFAs
Yuan Gao (The University of Western Ontario), Kai Salomaa (Queen's, University), Sheng Yu (The University of Western Ontario)
TL;DR
This paper investigates the transition complexity of incomplete deterministic finite automata for regular languages, revealing differences from state complexity in union and complementation, but similarities in intersection.
Contribution
It provides new insights into transition complexity for Boolean operations on incomplete DFAs, highlighting key differences and similarities with state complexity.
Findings
Transition complexity for union and complementation differs from state complexity.
Transition complexity for intersection aligns closely with state complexity.
Results enhance understanding of automata behavior in regular language operations.
Abstract
In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained. It is shown that the transition complexity results for union and complementation are very different from the state complexity results for the same operations. However, for intersection, the transition complexity result is similar to that of state complexity.
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