Showing papers on "ω-automaton published in 1988"
24 Oct 1988
TL;DR: The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case, and can be used to obtain an improved complementation construction for Buchi automata that is essentially optimal.
Abstract: Automata on infinite words were introduced by J.R. Buchi (1962) in order to give a decision procedure for S1S, the monadic second-order theory of one successor. D.E. Muller (1963) suggested deterministic omega -automata as a means of describing the behavior of nonstabilising circuits. R. McNaughton (1966) proved that classes of languages accepted by nondeterministic Buchi automata and by deterministic Muller automata are the same. His construction and its proof are quite complicated, and the blow-up of the construction is double exponential. The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case. This construction is essentially optimal. It can also be used to obtain an improved complementation construction for Buchi automata that is also optimal. Both constructions can be used to improve the complexity of decision procedures that use automata-theoretic techniques. >
551 citations
TL;DR: It is shown that some kind of meaningful computation can be embedded in very simple, microscopically homogeneous, one-dimensional automata, and in particular filter automata with a parity next-state rule.
Abstract: It is shown that some kind of meaningful computation can be embedded in very simple, microscopically homogeneous, one-dimensional automata, and in particular filter automata with a parity next-state rule. A systematic procedure is given for generating moving, periodic structures (particles). These particles exhibit soliton-like properties; that is, they often pass through one another with phase shifts. Ways to encode information in the phase of these particles are discussed. The search for useful logical operations is reduced to a search for paths in certain graphs. As a demonstration of principle, the details of implementing a carry-ripple adder are given. >
68 citations
07 Dec 1988
TL;DR: The clock automaton is a special type of automaton used for decreasing the real-time behavior of processes, controllers, and real- time specifications.
Abstract: A discrete-event process is modeled as a controlled state machine, in the framework of D.J. Ramadge and W.M. Wohman (1986). Their approach is extended to model a class of real-time discrete-event processes by means of a special type of automaton, called a clock automaton. The clock automaton is used for decreasing the real-time behavior of processes, controllers, and real-time specifications. >
46 citations
01 Jan 1988
27 citations
11 Jul 1988
TL;DR: It is shown that for any linear finite automaton M over a finite commutative ring with 1 the following statements are equivalent: M is weakly invertible, the transfer function matrix of M has a left inverse matrix, and there is a weak inverse linear infinite automaton of M.
Abstract: This paper deals with the invertibility problem of linear finite automata over a finite commutative ring with 1. It is shown that for any linear finite automaton M over a finite commutative ring with 1 the following statements are equivalent: 1. M is weakly invertible, 2. the transfer function matrix of M has a left inverse matrix, 3. there is a weak inverse linear finite automaton of M. And for linear finite automata over the ring of integers modulo q, this paper gives a decision procedure for an invertible (a weakly invertible, resp.) linear finite automaton with delay t and a construction method of its linear inverse (weak inverse, resp.) with delay t.
17 citations
TL;DR: This paper studies the ω-languages accepted by finite automata under a new type of accepting conditions which are based on whether the automaton enters all of its accepting states infinitely many times or not, and investigates the classes of υ-l languages defined thereby in relation to other well-known subclasses of the class of ω.
12 citations
TL;DR: Non-trivial correspondence in global structure is found between the state transition diagrams under the two rules: correspondence of cycle structure, basin volume of each cycle and structure of transient trees etc.
11 citations
TL;DR: The solution of the problem of finding which inputs for a function of discrete variables will result in any specified output for the set of binomially determined nearest neighbor additive cellular automata defined on finite or half-infinite sequences is reported.
Abstract: This paper reports the solution of the problem of finding which inputs for a function of discrete variables will result in any specified output for the set of binomially determined nearest neighbor additive cellular automata defined on finite or half-infinite sequences. In computing the solution to this problem a process which is the discrete analog to backward integration is defined. This process is determined in terms of an operator which exhibits an interesting period multiplying property.
9 citations
TL;DR: This paper presents a meta-analyses of automata in random environments and the analysis of the behaviour of infinite stochastic automata and games of Markov automata.
Abstract: CONTENTS Introduction § 1. Operation of automata in random environments § 2. Walks and the analysis of the behaviour of infinite stochastic automata § 3. Behaviour of finite automata § 4. Games of Markov automata Comments References
9 citations
TL;DR: Deterministic and nondeterministic automata on ω-strings have been studied extensively under six different acceptance conditions, but two of the conditions were not considered; the present paper completes the gap by showing that alternating Ϭ-automata accept precisely the υ-regular languages under these conditions.
Book•
01 Jan 1988
TL;DR: These models give a solution to the distribution problem of a set of sequential processes on several processors by model distributed processes by the computations of synchronized automata.
Abstract: We model distributed processes by the computations of synchronized automata. These machines are collections of finite automata the computations of which are linked through by synchronization states. With these models we give a solution to the distribution problem of a set of sequential processes on several processors.
11 Jul 1988
TL;DR: A new algorithm based on breadth first search that runs in faster asymptotic time than Natarajan's algorithms, and in addition finds the shortest possible reset sequence if such a sequence exists, and gives tight bounds on the length of the minimum reset sequence.
Abstract: Natarajan reduced the problem of designing a certain type of mechanical parts orienter to that of finding reset sequences for monotonic deterministic finite automata. He gave algorithms that in polynomial time either find such sequences or prove that no such sequence exists. In this paper we present a new algorithm based on breadth first search that runs in faster asymptotic time than Natarajan's algorithms, and in addition finds the shortest possible reset sequence if such a sequence exists. We give tight bounds on the length of the minimum reset sequence. We further improve the time and space bounds of another algorithm given by Natarajan, which finds reset sequences for arbitrary deterministic finite automata when all states are initially possible.
Book•
22 Jun 1988
TL;DR: An overview of the firing squad synchronization problem and representation of knowledge and learning on automata networks.
Abstract: An introduction to automata network theory.- Arrays, automata and groups - Some interconnections.- Local maps.- Threshold networks and generalizations.- Computation on finite networks of automata.- Systolic algorithms for path-finding problems.- An overview of the firing squad synchronization problem.- Representation of knowledge and learning on automata networks.- Random Boolean nets and disordered systems.
18 Nov 1988
TL;DR: The inverse map from approximation to the class of cellular automata approximated is constructed and the key matter is formatting the local structure theory equations in terms of block probability estimates weighted by coefficients.
Abstract: This is the second of two lectures. In the first lecture the map from a cellular automaton to a sequence of analytical approximations called the local structure theory was described. In this lecture the inverse map from approximation to the class of cellular automata approximated is constructed. The key matter is formatting the local structure theory equations in terms of block probability estimates weighted by coefficients. The inverse mapping relies on this format. Each possible assignment of values to the coefficients defines a class of automata with related statistical properties. It is suggested that these coefficients serve to smoothly parameterize the space of cellular automata. By varying the values of the parameters a cellular automaton network may be designed so that it has a specified invariant measure. If an invariant measure is considered a ''memory'' of the network, then this variation of parameters to specify the invariant measure must be considered ''learning.'' It is important to note that in this view learning is not the storage of patterns in a network, but rather the tailoring of the dynamics of a network. 7 figs.
TL;DR: A negative solution of counting problems for some classes slightly different from bounded arithmetic (,0 sets) is presented and properties of chains of finite automata are studied.
Abstract: In this paper we present a negative solution of counting problems for some classes slightly different from bounded arithmetic (,0 sets). To get the results we study properties of chains of finite automata. ?1. Basic definitions and discussion of the results. By finite automata we understand-one-way deterministic finite automata. We also assume that at each step of an execution finite automata move 1 position; they do not stop moving. Because of this assumption, if we employ several automata on the same input, they work synchronously and they read the same symbol at the same time. Because this works as in a real-time process we could refer to this symbol as to the current input signal. DEFINITION 1.1. (i) A k-automaton is a finite automaton using no more than k states. A p-counting automaton is a finite automaton with the states 0, 1,... , p 1 and the state transition function 6 such that for every state i and symbol x we have 6(x,i) = i + h(x)(modp), where h is a function associated with this automaton with rng h c {0, 1 }. Aut is a counting automaton if it is a p-counting automaton for some p. (ii) is a chain of finite automata iff the automata Autl,.. ., Autt have one common reading head moving to the left without stopping and for each j is a k-chain if Aut1,... , Autt are k-automata, i.e. IQ I = = IQtI = k. is a chain of k-automata and counting automata if for Received September 11, 1985; revised January 30, 1987. ? 1988, Association for Symbolic Logic 0022-4812/88/5301 -0020/$02.60
Posted Content•
TL;DR: In this paper, the authors examined the problem of finding a best-response automata for a player in a repeated game, and showed that the problem is relatively easy if the number of players is fixed, but "difficult" otherwise.
Abstract: The following problem is examined: given a game and the opponents' finite automata, find a best-response automaton for a certain player in the repeated game. It is shown that the problem is relatively "easy" (i.e., of polynomial time complexity) if the number of players is fixed, but "difficult" otherwise.
01 Feb 1988
TL;DR: Students can benefit from an earlier, informal exposure to finite automata for three reasons: - Finite automata represent a useful application when two-dimensional arrays are introduced, and a painless early introduction can ease the transition to rigorous approaches encountered later.
Abstract: In the computer science curriculum, finite state machines and finite automata are typically introduced at the upper-division level. However, students can benefit from an earlier, informal exposure to finite automata for three reasons:- Finite automata represent a useful application when two-dimensional arrays are introduced.- A painless early introduction can ease the transition to rigorous approaches encountered later.- Finite automata provide yet another algorithmic tool to be added to the student's repertoire.
TL;DR: The problems of computing the automorphism group of automata, testing either two graphs, two strongly connected automata for isomorphism, or two Automata for strong-isomorphism are shown to be polynomially equivalent.
Abstract: A polynomial time algorithm for computing the automorphism group of cyclic automata is given The problems of computing the automorphism group of automata, testing either two graphs, two strongly connected automata for isomorphism, or two automata for strong-isomorphism are shown to be polynomially equivalent
TL;DR: The necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographical Godel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set as mentioned in this paper.
Abstract: We prove that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographical Godel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.
TL;DR: A problem about intersections of languages accepted by finite automata is proposed and some partial results are given.