Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.Comment: 28 page

Testing the Equivalence of Regular Languages

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automata, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten

Using neural-computers for improving the control computers’s performance

Рассмотрены возможность и принципы использования нейровычислителей для повышения производительности бортовых вычислительных систем автоматического управления подвижными объектами.an opportunity and principles of using neural-computers for improving the performance of on-board evaluated control-automatic systems of mobile units are propose

Position Automaton Construction for Regular Expressions with Intersection

Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible with intersection. The resulting automaton is homogeneous and has the partial derivative automaton as its quotient

On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection

Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016

Consistency and Semantics of Equational Definitions over . . .

We introduce and study the notion of an equational definition over a predefined algebra (EDPA) which is a modification of the notion of an algebraic specification enrichment. We argue that the latter is not quite appropriate when dealing with partial functions (in particular, with those defined by non-terminating functional programs), and suggest EDPA as a more adequate tool for specification and verification purposes. Several results concerning consistency of enrichments and correctness of EDPA are presented. The relations between EDPA and some other approaches to algebraic specification of partial functions are discussed. 1 Introduction 1.1 Motivation Algebraic specification and term-rewriting methods seem very convenient to use in the following wide-spread situation: given a set A of data with several # On leave from the V. M. Glushkov Institute of Cybernetics, Kiev, Ukraine; predefined functions g 1 , . . . , g k on it, one needs to define (sometimes constructively) a set of n..

METHOD FOR RETROSPECTIVE DETERMINATION OF OBJECT MOVEMENT TRAJECTORY AND DEVICE FOR ITS IMPLEMENTATION

FIELD: radar systems. SUBSTANCE: invention relates to radar systems. The method of retrospective determination of the trajectory of an object's movement is characterized by the fact that using a radar receiver of the radar system, radar data about detected objects in previous sounding cycles are collected and stored for a certain period of time, at the initial time t = t0 a standard radar track of the object is formed based on the collected radar data update the standard radar track over a period of time. Each retrospectively built track of the object is assigned a lattice diagram; to obtain the current estimate of the path, only the set of the most plausible paths of the object is used, the most probable path is the path obtained at the current step with the lowest total estimate. A device for retrospective determination of the trajectory of an object has an antenna system associated with a controlled microwave transceiver microcircuit containing a generator connected to any of the n-transmitting antennas, an amplifier, the signal input of which is connected to any of the m-receiving antennas, and the signal output is connected to the first input of the mixer, the second signal input of the mixer is connected to the signal generator. EFFECT: reduced processing time for tracks from various moving objects. 3 cl, 3 dwg.Изобретение относится к радарным системам. Способ ретроспективного определения траектории движения объекта характеризуется тем, что с помощью радиолокационного приемника радиолокационной системы собирают и хранят радиолокационные данные о детектированных объектах в предыдущих циклах зондирования за некоторый промежуток времени, в начальный момент времени t=t0 формируют стандартный радиолокационный трек объекта на основе собранных радиолокационных данных, обновляют стандартный радиолокационный трек в течение определенного периода времени. Каждому выстраиваемому ретроспективно треку объекта ставят в соответствие решетчатую диаграмму, для получения текущей оценки пути используют только набор наиболее правдоподобных путей объекта, наиболее вероятным путём является полученный на текущем шаге путь, имеющий наименьшую суммарную оценку. Устройство для ретроспективного определения траектории движения объекта содержит антенную систему, связанную с управляемой микросхемой СВЧ-приёмопередатчика, содержащей генератор, подключаемый к любой из n-передающих антенн, усилитель, сигнальный вход которого подключается к любой из m-приемных антенн, а сигнальный выход подключен к первому входу смесителя, второй сигнальный вход смесителя подключен к генератору сигнала. Достигается сокращение времени обработки треков от различных подвижных объектов. 2 н. и 1 з.п. ф-лы, 3 ил