Showing papers on "Turing machine published in 1976"
TL;DR: In this article, a new formal model of register machines is described, which contain bit vectors which are manipulated using bitwise Boolean operations and shifts, and the main results relate the language recognition power of such vector machines to that of Turing machines, regardless of whether the machines are deterministic or non-deterministic.
120 citations
TL;DR: This paper presents further evidence in support of the conjecture that SP cannot be recognized using storage (log n)^k for any k, and proves the result for a suitably restricted device.
107 citations
TL;DR: The main results are (1) L(f) ≦ O(TC(L(f))), (2) TC(f), O(L (f)22+ɛ) for every ɛ ⋙ O.
Abstract: Let L(f) be the network complexity of a Boolean function L(f). For any n-ary Boolean function L(f) let $$TC(f) = min\{ T_p^{\bar A} (n){\text{ (}}\parallel p\parallel + 1gS_p^{\bar A} {\text{(}}n{\text{):}}res_p^{\bar A} {\text{(}}n{\text{) = }}f\} $$ . Hereby p ranges over all relative Turing programs and a? ranges over all oracles such that given the oracle a?, the restriction of p to inputs of length n is a program for L(f). ?p? is the number of instructions of p. T p a? (n) is the time bound and S p a? of the program p relative to the oracle a? on inputs of length n. Our main results are (1) L(f) ? O(TC(L(f))), (2) TC(f) ? O(L(f) 2 2+?) for every ? ? O.
98 citations
TL;DR: It is argued that human pattern recognition can be simulated by automata and it is shown that gestalt recognition and recognition of family resemblances are within the capabilities of sufficiently complex Turing machines.
Abstract: In this paper I argue that human pattern recognition can be simulated by automata. In particular, I show that gestalt recognition and recognition of family resemblances are within the capabilities of sufficiently complex Turing machines. The argument rests on elementary facts of automata and computability theory which are used to explicate our preanalytic, informal concepts concerning gestalt patterns and recognition. The central idea is that of a machine which "knows" its own structure. Although the paper thus aims to support mechanism, especially as a framework hypothesis for perception, it contains suggestions for philosophy of science and philosophy of language as well. Some of these suggestions are sketched in the final section.
35 citations
03 May 1976
TL;DR: This work uses a sufficient condition when an on-line algorithm can be transformed into a real-time algorithm to construct real- time algorithms for string-matching and palindrome recognition problems by random access machines and by Turing machines.
Abstract: We give a sufficient condition when an on-line algorithm can be transformed into a real-time algorithm. We use this condition to construct real-time algorithms for string-matching and palindrome recognition problems by random access machines and by Turing machines.
35 citations
06 Sep 1976
TL;DR: The paper attempts to present descriptional complexity as an identifiable part of the theory of complexity incorporating many diverse areas of research and discusses relation between descriptional and computational complexity.
Abstract: The paper attempts (i) to present descriptional complexity as an identifiable part of the theory of complexity incorporating many diverse areas of research, (ii) to formulate basic problems and to survey some results (especially those concerning languages) in descriptional complexity, (iii) to discuss relation between descriptional and computational complexity.
23 citations
TL;DR: In this paper, it was shown that any semirecursive η-hyperhypersimple set has partial Turing degree, i.e., the set has a constant number of elements.
Abstract: We shall establish that any semirecursive η-hyperhypersimple set has partial Turing degree.
17 citations
TL;DR: Their nonexistence results continue to hold even if the authors only ask that an optimizer behave properly when the input program P satisfies certain convergence properties and possesses an equivalent optimal program which is neither too hard nor too easy to compute.
10 citations
TL;DR: Metatheorems are presented which can be used to establish undecidability results about context-free grammar problems, and establish lower bounds on certain decidable grammar problems.
6 citations
01 Jan 1976
25 Oct 1976
TL;DR: In Part I, a linear-time on-line recognition algorithm for P1* ("palstar") on a random-access machine with addition and uniform cost criterion is presented and a lineartime on- line recognition algorithms for P12 on a multitape Turing machine and a recognition algorithm on a two-way deterministic pushdown automaton are presented.
Abstract: Let P1 = {w e Σ*:w = wR, |w| ≫ 1} be the set of all nontrivial palindromes over Σ. In Part I, we present a linear-time on-line recognition algorithm for P1* ("palstar") on a random-access machine with addition and uniform cost criterion. We also present a lineartime on-line recognition algorithm for P12 on a multitape Turing machine and a recognition algorithm for P12 on a two-way deterministic pushdown automaton. The correctness of these algorithms is based on new "cancellation lemmas" for the languages P1* and P12. In Part II, we present real-time recognition algorithms for the languages {wxyxz e Σ*: |w|=r|x|, |y|=s|x|, |z|=t|x|} and {wxyxRz e Σ*: |w|=r|x|, |y|=s|x|, |z|=t|x|} on multitape Turing machines, for arbitrary fixed r, s, and t.
13 Oct 1976
TL;DR: A first approximation to a design discipline for writing embedded AOLs is presented and the generalized transition table is introduced as a data structure in which finite-state machines, Turing machines, pushdown automata, and the like can be represented as special cases.
Abstract: Embedding is the extension of a programming language without altering the processor for that language, and preferably using only the facilities of that language. While a single subroutine is the simplest form of semantic extension by embedding, embedding can produce powerful application-oriented languages (AOL) in a relatively economical fashion.A first approximation to a design discipline for writing embedded AOLs is presented. SNOBOL4 is discussed as a particularly receptive host language, in that it has flexible subroutine, data-structure, and storage allocation facilities, has a run-time compiler which can be called from a SNOBOL4 program, and is widely available for almost all research computer systems.A description is given of AUTOMAT, a SNOBOL4-embedded AOL for classroom or research experiments with abstract sequential machines. The generalized transition table is introduced as a data structure in which finite-state machines (FSM), Turing machines, pushdown automata, and the like can be represented as special cases. Data structures for sets, partitions and covers, sparse matrices, and tapes are provided as well.The AUTOMAT AOL currently includes over 100 operators developed according to the proposed method. Applications thus far include an extensive FSM utility system, universal simulators for FSM and other models, FSM minimization, and Krohn-Rhodes decomposition. Performance statistics are presented.
TL;DR: For the recognition of context-free languages (CF-languages), use is made of Turing machines with two tapes: the input tape and the operational tape, which denotes the class of languages which are recognized on deterministic (nondeterministic) Turing Machines with L(n) ~< log2n.
Abstract: For the recognition of context-free languages (CF-languages), use is made of Turing machines with two tapes: the input tape and the operational tape. Let n be the length of the input tape. As a measure of complexity we choose the length of the operational tape L(n). We denote by M (respectively, N) the class of languages which are recognized on deterministic (nondeterministic) Turing machines with L(n) ~< log2n. It is known that all CF-languages enter in class N [4, 7] and are recognized by deterministic Turing machines with L(n) ~< (log2n) 2 [3], while class M contains certain subclasses of CF-languages (for example, the Dyck language, bounded CFlanguages [7]). It is also noted in [7] that all the examples of CF-languages known to the authors belong to class M. The following two problems are well known:
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TL;DR: It is shown that any function computed by a finite-state machine called a circular automata which processes information in a queue is computable (recognizable) by a Turing machine and vice versa and the class of languages recognized by (non-) deterministic linear bounded automata is equal to those which don't expand the length of the contents of the queue.
Abstract: We define a finite-state machine called a circular automata (CA) which processes information in a queue; we show that any function computed (or any language recognized) by such a machine is computable (recognizable) by a Turing machine and vice versa. Space and time bounds are given for the needed simulations. Furthermore, the class of languages recognized by (non-) deterministic linear bounded automata is equal to the class of languages recognized by (non-) deterministic CA which don't expand the length of the contents of the queue. Whether every language recognized by such a non-expanding CA is recognized by a deterministic one is equivalent to the famous LBA problem.CA can be viewed as generalizations of ordinary finite automata and as a Shepherdson-Sturgis single register machine programming language. An interesting model of a non-expanding CA is that of a finite-state machine which process tapes in the form of a loop. This appears to be a very natural way to process magnetic tape which circles back on itself.
TL;DR: A logical device which in essence is a Turing machine is described and an example of medical application is given and its response to a given stimulus depends on the experience it has had in the circuit in which it is placed.
Abstract: A logical device which in essence is a Turing machine is described and an example of medical application is given. Its response to a given stimulus depends on the experience it has had in the circuit in which it is placed.Cette note decrit un dispositif logigue. Dans son principe, ce depositif est une machine de Turing. Un exemple d'application medicale en est donne. Sa reponse a un stimulus depend de l'experience acquise. Cette experience est fonction de l'environnement dans lequel il est place.
01 Nov 1976
TL;DR: Two following papers (PB-69 and PB70) will contain detailed constructions and proofs for the upper and lower bounds on the time or memory required for solution by Turing machines.
Abstract: We study the computational complexity of some decidable systems. The problems are membership. emptiness and finiteness; the L systems are the ED0L, E0L, EDT0L and ET0L systems. For each problem and type of system we state both upper and lower bounds on the time or memory required for solution by Turing machines. Two following papers (PB-69 and PB70) will contain detailed constructions and proofs for the upper and lower bounds.
01 Jan 1976
TL;DR: In this chapter the authors shall give three versions of the notion of effectively calculable function: recursive functions (defined explicitly by means of closure conditions), an analogous but less redundant version due to Julia Robinson, and the idea of Turing computable function, based upon Turing machines.
Abstract: In this chapter we shall give three versions of the notion of effectively calculable function: recursive functions (defined explicitly by means of closure conditions), an analogous but less redundant version due to Julia Robinson, and the notion of Turing computable function, based upon Turing machines. These three notions will be shown to be equivalent; here the results of Chapters 1 and 2 serve as essential lemmas. In the exercises, three further equivalent notions are outlined: a variant of our official definition of recursiveness,the Godel-Herbrand-Kleene calculus, and a generalized computer version which is even closer to actual computers than Turing machines. As stated in the introduction to this part, none of these different versions stands out as overwhelmingly superior to the others in any reasonable way. The versions involving closure conditions are mathematically the simplest. The ones using generalized machines seem the most intuitively appealing. The Kleene calculus and the Markov algorithms of the next section are closest to the kinds of symbol manipulations and algorithmic procedures that one works out on paper or within natural languages. Take your pick.
TL;DR: It is shown that for n=1 even nondeterministic Turing assemblers have a sharply restricted computational capability, being able to successfully assemble only regular sets.
06 Sep 1976
01 Jan 1976
TL;DR: This chapter wants to survey, without proofs, some further topics of recursion theory that are also frequently useful in logical investigations.
Abstract: We have developed recursion theory as much as we need for our later purposes in logic. But in this chapter we want to survey, without proofs, some further topics. Most of these topics are also frequently useful in logical investigations.
06 Sep 1976