TL;DR: A fragment of the literature on queue automata is toured to give a comprehensive overview of fundamental results and recent developments.
Abstract: A queue automaton is basically a finite automaton equipped with a storage obeying the first-in-first-out principle, a queue. The power of queue automata has been studied from several perspectives. One of the classical results frequently cited in the literature is that a machine equipped with a queue storage can be capable of universal computations. This result has been discovered several times. At least implicitly it has already been mentioned by Post in 1943. In connection with formal languages, Vollmar studied in 1970 queue automata for the first time. Despite their versatility queue automata received only occasional attention, probably due to their high computational power with consequent low manageability. These facts triggered the study of subclasses and restricted variants of queue automata which documents the importance of these devices also from a practical point of view. In the present paper, we tour a fragment of the literature on queue automata to give a comprehensive overview of fundamental results and recent developments.
TL;DR: This work proves the preservation of regularity if the queue automaton loops through some special sets of transformation sequences, and proves that the construction is possible in polynomial time.
Abstract: We study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformation sequences. This is a generalization of the results by Boigelot et al. and Abdulla et al. regarding queue automata looping through a single sequence of transformations. We also prove that our construction is possible in polynomial time.
TL;DR: This work proves the preservation of regularity if the queue automaton loops through some special sets of transformations, which is a generalization of the results by Boigelot et al. regarding queue automata looping through a single sequence of transformations.
Abstract: We study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformations. This is a generalization of the results by Boigelot et al. and Abdulla et al. regarding queue automata looping through a single sequence of transformations. We also prove that our construction is effective and efficient.
TL;DR: In this article, the authors consider the notion of a constant length queue automaton (i.e., a traditional queue automata with a built-in constant limit on the length of its queue) as a formalism for representing regular languages.
Abstract: We consider the notion of a constant length queue automaton—i.e., a traditional queue automaton with a built-in constant limit on the length of its queue—as a formalism for representing regular languages. We show that the descriptional power of constant length queue automata greatly outperforms that of traditional finite state automata, of constant height pushdown automata, and of straight line programs for regular expressions, by providing optimal exponential and double-exponential size gaps. Moreover, we prove that constant height pushdown automata can be simulated by constant length queue automata paying only by a linear size increase, and that removing nondeterminism in constant length queue automata requires an optimal exponential size blow-up, against the optimal double-exponential cost for determinizing constant height pushdown automata. Finally, we investigate the size cost of implementing Boolean language operations on deterministic and nondeterministic constant length queue automata.