Abstract
We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.
Highlights
The operation problem for a language family is the question of costs of operations on languages from this family with respect to their representations
More than two decades ago, the operation problem for regular languages represented by deterministic finite automata as studied in [14,15] renewed the interest in descriptional complexity issues of finite automata in general
In order to compare the operational state complexities of deterministic undirected finite automata (DUFA) and nondeterministic undirected finite automata (NUFA) with classical deterministic and nondeterministic finite automata, we summarize the latter complexities in
Summary
The operation problem for a language family is the question of costs (in terms of states) of operations on languages from this family with respect to their representations. Impressively many results have been obtained for a large number of language families It seems that the recent studies of operational state complexity focus on subregular languages. Examples of early studied classes are finite languages, definite languages and variants, star-free languages, etc Some of these regular subfamilies were motivated by particular issues such as, for instance, neural nets or circuit. We are interested in a strict form of reversible finite automata, namely we do require that every state of the automaton has a unique predecessor for a given input letter, but that this predecessor can already be reached by a forward transition with the same input letter.
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