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Thinking May Be More Than Computing
 Cognition
, 1986
"... The uncomputable parts of thinking (if there are any) can be studied in much the same spirit that Turing (1950) suggested for the study of its computable parts. We can develop precise accounts of cognitive processes that, although they involve more than computing, can still be modelled on the machin ..."
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Cited by 18 (3 self)
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The uncomputable parts of thinking (if there are any) can be studied in much the same spirit that Turing (1950) suggested for the study of its computable parts. We can develop precise accounts of cognitive processes that, although they involve more than computing, can still be modelled on the machines we call ‘computers’. In this paper, I want to suggest some ways that this might be done, using ideas from the mathematical theory of uncomputability (or Recursion Theory). And I want to suggest some uses to which the resulting models might be put. (The reader more interested in the models and their uses than the mathematics and its theorems, might want to skim or skip the mathematical parts.) 1.
The ChurchTuring Thesis over Arbitrary Domains
, 2008
"... The ChurchTuring Thesis has been the subject of many variations and interpretations over the years. Specifically, there are versions that refer only to functions over the natural numbers (as Church and Kleene did), while others refer to functions over arbitrary domains (as Turing intended). Our pu ..."
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Cited by 12 (9 self)
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The ChurchTuring Thesis has been the subject of many variations and interpretations over the years. Specifically, there are versions that refer only to functions over the natural numbers (as Church and Kleene did), while others refer to functions over arbitrary domains (as Turing intended). Our purpose is to formalize and analyze the thesis when referring to functions over arbitrary domains. First, we must handle the issue of domain representation. We show that, prima facie, the thesis is not well defined for arbitrary domains, since the choice of representation of the domain might have a nontrivial influence. We overcome this problem in two steps: (1) phrasing the thesis for entire computational models, rather than for a single function; and (2) proving a “completeness” property of the recursive functions and Turing machines with respect to domain representations. In the second part, we propose an axiomatization of an “effective model of computation” over an arbitrary countable domain. This axiomatization is based on Gurevich’s postulates for sequential algorithms. A proof is provided showing that all models satisfying these axioms, regardless of underlying data structure, are of equivalent computational power to, or weaker than, Turing machines.
Three Paths to Effectiveness
"... For Yuri, profound thinker, esteemed expositor, and treasured friend. Abstract. Over the past two decades, Gurevich and his colleagues have developed axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in a new framework of abstract state ..."
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Cited by 4 (4 self)
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For Yuri, profound thinker, esteemed expositor, and treasured friend. Abstract. Over the past two decades, Gurevich and his colleagues have developed axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in a new framework of abstract state machines. Recently, this approach was extended to suggest axiomatic foundations for the notion of effective computation over arbitrary countable domains. This was accomplished in three different ways, leading to three, seemingly disparate, notions of effectiveness. We show that, though having taken different routes, they all actually lead to precisely the same concept. With this concept of effectiveness, we establish that there is – up to isomorphism – exactly one maximal effective model across all countable domains.
When is a computer not a computer?
"... We recently bought an IBMBLOKBUSTR computer, after reading Osherson’s (1985) beguiling description of its ability to do the uncomputable. We had hoped to use it in our study of the human ability to generate music. But we ran into problems that we had not anticipated. Readers of this journal who pla ..."
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We recently bought an IBMBLOKBUSTR computer, after reading Osherson’s (1985) beguiling description of its ability to do the uncomputable. We had hoped to use it in our study of the human ability to generate music. But we ran into problems that we had not anticipated. Readers of this journal who plan to use this rather unusual machine in their research, might want to profit from our experience. What makes BLOKBUSTR different from other computers is that it can do more than compute. For example, it can run a program, KBAR, that outputs all and only the integers in the set that mathematicians call “Kbar”. Kbar is uncomputable. It consists of the indexes of Turing machines that do not halt when run on their own indexes. Since we can provemathematicallythat this set cannot be generated by a computation, BLOKBUSTR can do something no ordinary computer can. In our lab, we feel that some human cognitive abilities require more than computing. The ability to generate and recognize good music, for example.
Part I The art of logic 1 Chapter 1
"... After some preliminary grammatical considerations in this chapter, we collect the material on truthfunctional logic in chapter 2; the material on quantifiers and identity in chapter 3 (proofs), chapter 5 (symbolization), and chapter 6 (semantics); some applications in chapter 7 (logical theory, ari ..."
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After some preliminary grammatical considerations in this chapter, we collect the material on truthfunctional logic in chapter 2; the material on quantifiers and identity in chapter 3 (proofs), chapter 5 (symbolization), and chapter 6 (semantics); some applications in chapter 7 (logical theory, arithmetic, set theory), and a discussion of definitions in chapter 8. Chapter 13 is an unfulfilled promise of a discussion of the chief theorems about modern logic.
Review Indigo: a WorldWideWeb review of genomes and gene functions
"... The present article describes a genome database reviewing generelated knowledge of two model bacteria, Bacillus subtilis and Escherichia coli. The database, Indigo, is open through the WorldWide Web ..."
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The present article describes a genome database reviewing generelated knowledge of two model bacteria, Bacillus subtilis and Escherichia coli. The database, Indigo, is open through the WorldWide Web
DOI:10.1111/j.15746976.2008.00137.x
, 2008
"... minimal genome; operating system; algorithmic complexity; junk DNA; APOBEC; ADAR. Various efforts to integrate biological knowledge into networks of interactions have produced a lively microbial systems biology. Putting molecular biology and computer sciences in perspective, we review another trend ..."
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minimal genome; operating system; algorithmic complexity; junk DNA; APOBEC; ADAR. Various efforts to integrate biological knowledge into networks of interactions have produced a lively microbial systems biology. Putting molecular biology and computer sciences in perspective, we review another trend in systems biology, in which recursivity and information replace the usual concepts of differential equations, feedback and feedforward loops and the like. Noting that the processes of gene expression separate the genome from the cell machinery, we analyse the role of the separation between machine and program in computers. However, computers do not make computers. For cells to make cells requires a specific organization of the genetic program, which we investigate using available knowledge. Microbial genomes are organized into a paleome (the name emphasizes the role of the corresponding functions from the time of the origin of life), comprising a constructor and a replicator, and a cenome (emphasizing communityrelevant genes), made up of genes that permit life in a particular context. The cell duplication process supposes rejuvenation of the machine and replication of the program. The paleome also possesses genes that enable information to accumulate in a ratchetlike process down the generations. The systems biology must include the dynamics of information creation in its future developments.