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Automated generation of readable proofs with geometric invariants, II. Theorem proving with fullangles
 J. Automated Reasoning
, 1996
"... Abstract. In this series of papers, we discuss how to use a fixed set of high level geometry lemmas or rules related to geometric invariants, such as area, fullangle, etc., to produce short and humanreadable proofs in geometry, especially to produce multiple and shortest proofs of a given geometry ..."
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Cited by 22 (3 self)
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Abstract. In this series of papers, we discuss how to use a fixed set of high level geometry lemmas or rules related to geometric invariants, such as area, fullangle, etc., to produce short and humanreadable proofs in geometry, especially to produce multiple and shortest proofs of a given geometry theorem. These rules are proved to be much more effective and concise than the rules based on triangle congruence used in related work before. The success of our approach is partially due to a skillful selection of geometric invariants and the related rules. Control and search strategies are proposed and experimented with to enhance the efficiency of the prover. In part I of this series, the high level geometry lemmas are about area and the CevaMenelaus configurations.
Toward a Viable, SelfReproducing Universal Computer
 Physica D
, 1996
"... Selfreproducing, cellular automatabased systems developed to date broadly fall under two categories; the first consists of machines which are capable of performing elaborate tasks, yet are too complex to simulate, while the second consists of extremely simple machines which can be entirely impleme ..."
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Cited by 20 (1 self)
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Selfreproducing, cellular automatabased systems developed to date broadly fall under two categories; the first consists of machines which are capable of performing elaborate tasks, yet are too complex to simulate, while the second consists of extremely simple machines which can be entirely implemented, yet lack any additional functionality aside from selfreproduction. In this paper we present a selfreproducing system which is completely realizable, while capable of executing any desired program, thereby exhibiting universal computation. Our starting point is a simple selfreproducing loop structure onto which we "attach" an executable program (Turing machine) along with its data. The three parts of our system (loop, program, data) are all reproduced, after which the program is run on the given data. The system reported in this paper has been simulated in its entirety; thus, we attain a viable, selfreproducing machine with programmable capabilities. 1 Introduction The study of art...
Constructing Evolutionary Systems On A Simple Deterministic Cellular Automata Space
, 1998
"... We succeeded for the first time in constructing evolutionary systems on a simple 9state 5neighbor cellular automata (CA) space by utilizing Langton's selfreproducing loop. CA are deterministic dynamical systems capable of representing extremely complex nonlinear phenomena, where time, space and s ..."
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Cited by 15 (3 self)
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We succeeded for the first time in constructing evolutionary systems on a simple 9state 5neighbor cellular automata (CA) space by utilizing Langton's selfreproducing loop. CA are deterministic dynamical systems capable of representing extremely complex nonlinear phenomena, where time, space and states of sites are all discrete. Many CA models of selfreproductive behavior of theoretical organisms have so far been energetically studied, but the evolutionary process of organisms driven by variation and natural selection has never been realized on CA space yet. In this dissertation, we added three improvements into Langton's loop, i.e., to realize a kind of death by introducing a new dissolving state `8' into the set of states of the CA, to enhance the adaptability (a degree of the variety of situations in which the structures in the CA space can operate regularly) of the selfreproductive mechanism described by the statetransition rules of the CA, and to modify the initial structure o...
The complexity of small universal Turing machines: a survey
, 2007
"... We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are e ..."
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Cited by 4 (2 self)
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We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. As a related result we also find that Rule 110, a wellknown elementary cellular automaton, is also efficiently universal. We also mention some old and new universal programsize results, including new small universal Turing machines and new weakly, and semiweakly, universal Turing machines. We then discuss some ideas for future work arising out of these, and other, results.
from Turing to Dijkstra”
"... Turing’s involvement with computer building was popularized in the 1970s and later. Most notable are the books by Brian Randell (1973), Andrew Hodges (1983), and Martin Davis (2000). A central question is whether John von Neumann was influenced by Turing’s 1936 paper when he helped build the EDVAC m ..."
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Turing’s involvement with computer building was popularized in the 1970s and later. Most notable are the books by Brian Randell (1973), Andrew Hodges (1983), and Martin Davis (2000). A central question is whether John von Neumann was influenced by Turing’s 1936 paper when he helped build the EDVAC machine, even though he never cited Turing’s work. This question remains unsettled up till this day. As remarked by Charles Petzold, one standard history barely mentions Turing, while the other, written by a logician, makes Turing a key player. Contrast these observations then with the fact that Turing’s 1936 paper was cited and heavily discussed in 1959 among computer programmers. In 1966, the first Turing award was given to a programmer, not a computer builder, as were several subsequent Turing awards. An historical investigation of Turing’s influence on computing, presented here, shows that Turing’s 1936 notion of universality became increasingly relevant among programmers during the 1950s. The central thesis of this paper states that Turing’s influence was felt more in programming after his death than in computer building during the 1940s. 1
Communicated
"... Sexual reproduction is modeled and investigated in the formal framework of John von Neumann’s theory of selfreproducing cellular automata. It is argued that the transition from asexual to sexual reproduction necessitates a change in number and structure of the genetic tapes involved. To an asexuall ..."
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Sexual reproduction is modeled and investigated in the formal framework of John von Neumann’s theory of selfreproducing cellular automata. It is argued that the transition from asexual to sexual reproduction necessitates a change in number and structure of the genetic tapes involved. To an asexually reproducing cellular automaton only one genetic tape is attached, viz. the description which enables the automaton to construct cell for cell a replica of itself. The sexually reproducing automaton, however, must possess two, nearly identical, genetic tapes of a deviating structure, i.e. programs partitioned into sections embodying the various construction and behavioral algorithms to be executed. It is shown that the recombination of the parents ’ characteristics in the offspring closely conforms to recombination in nature. Similarities and differences with biological systems are discussed. 1.
Contents
"... Abstract. In search of a single number like Shannon’s statesymbol product to compare the complicacy of Turing Machines including those with multiple tapes and tape heads, a number called TM index is proposed, using a generic definition for single and multi tape machines. Several examples are shown ..."
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Abstract. In search of a single number like Shannon’s statesymbol product to compare the complicacy of Turing Machines including those with multiple tapes and tape heads, a number called TM index is proposed, using a generic definition for single and multi tape machines. Several examples are shown together with their TM indices, including the recently rediscovered physical