New Type Of Automaton Research Articles

РАЗРАБОТКА МОДЕЛИ BP-СХЕМЫ НА ОСНОВЕ ТЕОРИИ АВТОМАТОВ И С ПРИМЕНЕНИЕМ МЕТОДОВ КВАНТОВОГО ПРОГРАММИРОВАНИЯ

The paper describes the concept of a new type of abstract automata “BP-scheme” (Business Process) that effectively distributes management commands between entities with their permanent growth in the paradigm of complexly modelled systems. The paper investigates the proposed model of the BP-scheme implementation, which is an artificial neural network, functioning based on fuzzy logic rules using the Takagi-Sugeno algorithm, for deriving rules in the form of functional dependencies. The model uses QPU (Quantum Processing Unit) in computing system behaviour, which implies a quick response to changes in the system entities. QPU used taking into account the developed rules of fuzzy neural network allows improving scenarios and predictive models of a complex system behaviour.

Fast Coalgebraic Bisimilarity Minimization

Coalgebraic bisimilarity minimization generalizes classical automaton minimization to a large class of automata whose transition structure is specified by a functor, subsuming strong, weighted, and probabilistic bisimilarity. This offers the enticing possibility of turning bisimilarity minimization into an off-the-shelf technology, without having to develop a new algorithm for each new type of automaton. Unfortunately, there is no existing algorithm that is fully general, efficient, and able to handle large systems. We present a generic algorithm that minimizes coalgebras over an arbitrary functor in the category of sets as long as the action on morphisms is sufficiently computable. The functor makes at most O ( m log n ) calls to the functor-specific action, where n is the number of states and m is the number of transitions in the coalgebra. While more specialized algorithms can be asymptotically faster than our algorithm (usually by a factor of ( m / n )), our algorithm is especially well suited to efficient implementation, and our tool often uses much less time and memory on existing benchmarks, and can handle larger automata, despite being more generic.

Weighted simple reset pushdown automata

We define a new normal form for weighted pushdown automata. The new type of automaton uses a stack but has only limited access to it. Only three stack commands are available: popping a symbol, pushing a symbol or leaving the stack unaltered. Additionally, ϵ-transitions are not used. We prove that this automaton model can recognize all weighted context-free languages (i.e., generates all algebraic power series).

ALTERNATING REGULAR TREE GRAMMARS IN THE FRAMEWORK OF LATTICE-VALUED LOGIC

In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued) regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is taken over to prove a main theorem: the class of languages generated by an {L}valued alternating regular tree grammar {LAG}) is equal to the class of languages accepted by an {L}valued alternating top-down tree automaton {LAA}). The second way is taken over to define a new type of automaton by combining the {L}valued alternating top-down tree automaton with stack, called {L}-valued alternating stack tree automaton {LASA} and the generative power of it is compared to some well-known language classes, especially to {LAA} and to {LAG}Also, we have derived a characterization of the state alternating regular tree grammar {LSAG}) in terms of {LASA}.

The ins and outs of first-order runtime verification

The main purpose of this paper is to introduce a first-order temporal logic, $${{\mathrm{LTL}}}^{{{{{\mathrm{FO}}}}}} $$LTLFO, and a corresponding monitor construction based on a new type of automaton, called spawning automaton. Specifically, we show that monitoring a specification in $${{\mathrm{LTL}}}^{{{{{\mathrm{FO}}}}}} $$LTLFO boils down to an undecidable decision problem. The proof of this result revolves around specific ideas on what we consider a "proper" monitor. As these ideas are general, we outline them first in the setting of standard LTL, before lifting them to the setting of first-order logic and $${{\mathrm{LTL}}}^{{{{{\mathrm{FO}}}}}} $$LTLFO. Although due to the above result one cannot hope to obtain a complete monitor for $${{\mathrm{LTL}}}^{{{{{\mathrm{FO}}}}}} $$LTLFO, we prove the soundness of our automata-based construction and give experimental results from an implementation. These seem to substantiate our hypothesis that the automata-based construction leads to efficient runtime monitors whose size does not grow with increasing trace lengths (as is often observed in similar approaches). However, we also discuss formulae for which growth is unavoidable, irrespective of the chosen monitoring approach. Specifically, we provide a general categorisation of so called monitorable languages, which is closely related to this notion of "growth-inducing" (that is, trace-length dependent) formulae. It relates to the well-known safety-progress hierarchy, yet is orthogonal to it.

New types of automata to solve fixed point problems

The aim of this article is to find the supremum of {X|AX⊆X∪B and X⊆K}, where A,B and K are three fixed, rational languages. This problem and its solution are formally inspired by retroaction in control theory. To get the solution, we introduce a new type of automata whose acceptance condition is a positive boolean formula. The time complexity of our algorithm depends linearly on the size of A, quadratically on the size of K and exponentially on the size of B, where the size is measured by the number of states of the minimal automaton.

Preset two-head automata and morphological analysis of natural language∗

Modeling the morphological structure of natural languages in terms of a nondeterministic finite-state automaton is shown to be inadequate in its handling of some common natural language phenomena. We show that a two-tape nondeterministic automaton is capable of handling these phenomena. The modeling is improved by the specification of a new type of automaton, the preset two-head automaton, which we argue is equivalent in expressive power to a linear context-free grammar. We discuss the operation of a parser which implements the improved model.

Tree pushdown automata

This paper presents a new type of automaton called a tree pushdown automaton (a bottom-up tree automaton augmented with internal memory in the form of a tree, similar to the way a stack is added to a finite state machine to produce a pushdown automaton) and shows that the class of languages recognized by such automata is identical to the class of context-free tree languages.

Two-dimensional automata with rotated inputs (projection-type)

This paper introduces a new type of automaton on a two-dimensional tape, which decides acceptance or rejection of an input tape x by first scanning the tape x from various sides with parallel/sequential array readers, and by then scanning the pair of the halting state configurations (i.e., projections) generated by these array readers with a multitape finite automaton. We mainly concentrate on investigating the accepting power of two-dimensional automata which consist of one-way parallel/sequential array readers and a multitape finite automaton operating in real time.

Two-dimensional automata with rotated inputs

This paper introduces a new type of automata on a two-dimensional tape, which decides acceptance or rejection of an input tape x by scanning the tape x from various sides by various automata. The accepting power of such an automaton is investigated. This paper mainly concentrates on investigating the accepting power of two-dimensional automata which consist of four parallel/sequential array automata, say M 1, M 2, M 3, and M 4, and which accept an input tape x if and only if x, x R , ( x R ) R , and (( x R ) R ) R are accepted by M 1, M 2, M 3, and M 4, respectively, where for any tape y, y R is the tape obtained by rotating y clockwise 90°.