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On minimality and size reduction of onetape and multitape finite automata
, 2004
"... In this thesis, we consider minimality and size reduction issues of onetape and multitape automata. Although the topic of minimization of onetape automata has been widely studied for many years, it seems that some issues have not gained attention. One of these issues concerns finding specific cond ..."
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In this thesis, we consider minimality and size reduction issues of onetape and multitape automata. Although the topic of minimization of onetape automata has been widely studied for many years, it seems that some issues have not gained attention. One of these issues concerns finding specific
COMPUTABILITY OF THE ENTROPY OF ONETAPE TURING MACHINES
, 2013
"... Abstract. We prove that the maximum speed and the entropy of a onetape Turing machine are computable, in the sense that we can approximate them to any given precision ǫ. This is contrary to popular belief, as all dynamical properties are usually undecidable for Turing machines. The result is quite ..."
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Abstract. We prove that the maximum speed and the entropy of a onetape Turing machine are computable, in the sense that we can approximate them to any given precision ǫ. This is contrary to popular belief, as all dynamical properties are usually undecidable for Turing machines. The result is quite
Theory of one tape linear time Turing machines
 Proc. 30th SOFSEM Conference on Current Trends in Theory and Practice of Computer Science, Lecture Notes in Computer Science, Vol.2932, pp.335–348
, 2004
"... Abstract. A theory of onetape lineartime Turing machines is quite different from its polynomialtime counterpart. This paper discusses the computational complexity of onetape Turing machines of various machine types (deterministic, nondeterministic, reversible, alternating, probabilistic, countin ..."
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, counting, and quantum Turing machines) that halt in time O(n), where the running time of a machine is defined as the height of its computation tree. We also address a close connection between onetape lineartime Turing machines and finite state automata. §1. Model of Computation: Turing Machines. We use a
Nondeterministic OneTape OffLine Turing Machines and Their Time Complexity
, 2009
"... In this paper we consider the time and the crossing sequence complexities of onetape offline Turing machines. We show that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n log n, in the case all accepting computations are considered (accept m ..."
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In this paper we consider the time and the crossing sequence complexities of onetape offline Turing machines. We show that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n log n, in the case all accepting computations are considered (accept
Sketchpad: A manmachine graphical communication system
, 2003
"... The Sketchpad system uses drawing as a novel communication medium for a computer. The system contains input, output, and computation programs which enable it to interpret information drawn directly on a computer display. It has been used to draw electrical, mechanical, scientific, mathematical, and ..."
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Cited by 702 (6 self)
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The Sketchpad system uses drawing as a novel communication medium for a computer. The system contains input, output, and computation programs which enable it to interpret information drawn directly on a computer display. It has been used to draw electrical, mechanical, scientific, mathematical, and animated drawings; it is a general purpose system. Sketchpad has shown the most usefulness as an aid to the understanding of processes, such as the notion of linkages, which can be described with pictures. Sketchpad also makes it easy to draw highly repetitive or highly accurate drawings and to change drawings previously drawn with it. The many drawings in this thesis were all made with Sketchpad.
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science Depa ..."
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Cited by 452 (3 self)
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this formalism has advantages both as a programming language and as a vehicle for developing a theory of computation. Next, we describe Sexpressions and Sfunctions, give some examples, and then describe the universal Sfunction apply which plays the theoretical role of a universal Turing machine
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 850 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]
Semantics of ContextFree Languages
 In Mathematical Systems Theory
, 1968
"... "Meaning " may be assigned to a string in a contextfree language by defining "attributes " of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of th ..."
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"Meaning " may be assigned to a string in a contextfree language by defining "attributes " of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are "synthesized", i.e., defined solely in terms of attributes of the descendants of the corresponding nonterminal symbol, while other attributes are "inherited", i.e., defined in terms of attributes of the ancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature. A simple technique for specifying the "meaning " of languages defined by contextfree grammars is introduced in Section 1 of this paper, and its basic mathematical properties are investigated in Sections 2 and 3. An example which indicates how the technique can be applied to the formal definition of programming languages i described in Section 4, and finally, Section 5 contains a somewhat biased comparison of the present method to other known techniques for semantic definition. The discussion in this paper is oriented primarily towards programming languages, but the same methods appear to be relevant also in the study of natural anguages. 1. Introduction. Let
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