Familles de langages fermees par crochet ouvert

AbstractWe present a new unary operator, the open bracket, and establish it has properties similar to the ones of the bracket of [1] and the syntactic operators of [10]. We can thus study an infinite hierarchy of checking automata languages

Self-regulating finite automata

This paper introduces and discusses self-regulating finite automata. In essence, these automata regulate the use of their rules by a sequence of rules applied during previous moves. A special attention is paid to turns defined as moves during which a self-regulating finite automaton starts a new self-regulating sequence of moves. Based on the number of turns, the present paper establishes two infinite hierarchies of language families resulting from two variants of these automata. In addition, it demonstrates that these hierarchies coincide with the hierarchies resulting from parallel right linear grammars and right linear simple matrix grammars, so the self-regulating finite automata can be viewed as the automaton counterparts to these grammars. Finally, this paper compares both infinite hierarchies. In addition, as an open problem area, it suggests the discussion of self-regulating pushdown automata and points out that they give rise to no infinite hierarchy analogical to the achieved hierarchies resulting from the self-regulating finite automata

Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results

On pure multi-pushdown automata that perform complete pushdown pops

This paper introduces and discusses pure multi-pushdown automata that remove symbols from their pushdowns only by performing complete pushdown pops. This means that during a pop operation, the entire pushdown is compared with a prefix of the input, and if they match, the whole contents of the pushdown is erased and the input is advanced by the prefix. The paper proves that these automata define an infinite hierarchy of language families identical with the infinite hierarchy of language families resulting from right linear simple matrix grammars. In addition, this paper discusses some other extensions of these automata with respect to operations they can perform with their pushdowns. More specifically, it discusses pure multi-pushdown automata that perform complete pushdown pops that are allowed to join two pushdowns and/or create a new pushdown

Reset machines

AbstractA reset tape has one read-write head which moves only left-to-right except that the head can be reset once to the left end and the tape rescanned; a multiple-reset machine has reset tapes as auxiliary storage and a one-way input tape. Linear time is no more powerful than real time for nondeterministic multiple-reset machines and so the family MULTI-RESET of languages accepted in real time by nondeterministic multiple-reset machines is closed under linear erasing. MULTI-RESET is closed under Kleene. It can be characterized as the smallest family of languages containing the regular sets and closed under intersection and linear-erasing homomorphic duplication or as the smallest intersection-closed semiAFL containing COPY = {ww | w in {a, b}∗}. A circular tape is read full-sweep from left-to-right only and then reset to the left, any number of times; a nonwriting circular tape cannot be altered after the first sweep. For nondeterministic machines operating in real time, multiple reset tapes, circular tapes or nonwriting circular tapes have the same power. Languages in MULTI-RESET can be accepted in real time by nondeterministic machines using only three reset tapes or using only one reset tape and one nonwriting circular tape

Regulated Formal Models and Their Reduction

Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult