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Turing Machines with Atoms

2013
*
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
*

We study

doi:10.1109/lics.2013.24
dblp:conf/lics/BojanczykKLT13
fatcat:bntizruis5bezdfgmwuemw7jje
*Turing**machines*over sets*with**atoms*, also known as nominal sets. ... Our main result is that deterministic*machines*are weaker than nondeterministic ones; in particular, P =NP in sets*with**atoms*. ...*Turing**machine**with**atoms*. ...##
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Turing machines with atoms, constraint satisfaction problems, and descriptive complexity

2014
*
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14
*

We study deterministic computability over sets

doi:10.1145/2603088.2603135
dblp:conf/csl/KlinLOT14
fatcat:whpzig7cnbhlzogjpkqpsuczbq
*with**atoms*. We characterize those alphabets for which*Turing**machines**with**atoms*determinize. ... Acknowledgments We are grateful to Marcin Kozik for guiding us in the land of Constraint Satisfaction Problems, to Mikołaj Bojańczyk for inspiring discussions on sets*with**atoms*, and to anonymous reviewers ...*Turing**machines*. Following [4] , a*Turing**machine**with**atoms*(TMA) is defined exactly as an ordinary*Turing**machine*, but*with*finite sets replaced by orbit-finite sets*with**atoms*. ...##
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Super Turing-machines

1998
*
Complexity
*

He described these as 'a new kind of

doi:10.1002/(sici)1099-0526(199809/10)4:1<30::aid-cplx9>3.0.co;2-8
fatcat:gg4ioowwtvhktfh7pnj4ql7dhy
*machine*' and called them 'O-*machines*'. An O-*machine*is a universal*Turing**machine*augmented*with*a 'black box'. ... Any universal*Turing**machine*can be programmed to carry out any calculation that can be performed by a human mathematician working*with*paper and pencil in accordance*with*some algorithmic method. ...##
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Degrees of Transducibility
[chapter]

2015
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Lecture Notes in Computer Science
*

As transformational devices, we focus here on

doi:10.1007/978-3-319-23660-5_1
fatcat:57hl6axxanbi7gqagwhifm5dru
*Turing**Machines*, sequential finite state transducers and Mealy*Machines*. ... In contrast*with*the degrees of unsolvability, very little is known about the structure of degrees obtained from finite state transducers or Mealy*Machines*. ... In Section 2, we start*with*the formal definition of the three main notions of degrees, as generated by transducibility using*Turing**Machines*, by sequential finite state transducers, and by Mealy*Machines*...##
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Reactive Turing Machines with Infinite Alphabets
[article]

2017
*
arXiv
*
pre-print

The notion of Reactive

arXiv:1610.06552v3
fatcat:l4yvkjifdvc27grzpry4iiewt4
*Turing**machine*(RTM) was proposed as an orthogonal extension of*Turing**machines**with*interaction. ... We propose a notion of of nominal executability based on RTMs*with**atoms*, and show that every effective transition system*with**atoms*is nominally executable. ... We define RTMs*with**atoms*as an extension of*Turing**machines**with**atoms*. ...##
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Finitely unstable theories and computational complexity
[article]

2014
*
arXiv
*
pre-print

iff the

arXiv:1410.4925v1
fatcat:opzk733isfcntgssmcepys4e7q
*Turing**machine*accepts its input. ... Both theorems involve encoding a*Turing**machine*by a formula in the corresponding logic and stating that a model of this formula exists if and only if the*Turing**machine*halts, i.e. the formula is satisfiable ...*Atoms*. From now on, we shall assume that our*Turing**machine*T is deterministic. ...##
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Quantum Speed‐up of Computations

2002
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Philosophy of Science
*

Consequently, one can physically 'realize' a universal

doi:10.1086/341843
fatcat:zf6rh63d4jgpzenyci2es63v4a
*Turing**machine*as a billiard*with*hyperbolic mirrors (Moore 1990; Pitowsky 1994) . ... Indeed, every step that a*Turing**machine*takes can be identified and checked. ...*Turing*provided us*with*an excellent conceptual tool for the analysis of the theoretical properties of algorithms, but it seems to be the wrong tool for the analysis of physical processes. ...##
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Atoms and Energy . H. W. S. Massey. Philosophical Library, New York, 1956. 174 pp. Illus. $4.75

1956
*
Science
*

- tions defined by

doi:10.1126/science.124.3220.493-a
fatcat:yw3j6sojnvbz7p5rh2u3mjv3i4
*Turing**machines*, and the fourth*with*the influence of unre- liable elements on*Turing*computability. ... The papers of the second part represent advances in the now well-known theory of*Turing**machines*, The first two papers deal*with*universal*Turing**machines*, the third*with*the question of inversion of func ...##
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Atoms and Energy . H. W. S. Massey. Philosophical Library, New York, 1956. 174 pp. Illus. $4.75

1956
*
Science
*

- tions defined by

doi:10.1126/science.124.3220.493.a
fatcat:k4nob5guhzhi7asrc6ivcuu6n4
*Turing**machines*, and the fourth*with*the influence of unre- liable elements on*Turing*computability. ... The papers of the second part represent advances in the now well-known theory of*Turing**machines*, The first two papers deal*with*universal*Turing**machines*, the third*with*the question of inversion of func ...##
###
Automata Studies . C. E. Shannon and H. McCarthy. Princeton University Press, Princeton, N.J., 1956. 285 pp. $4

1956
*
Science
*

- tions defined by

doi:10.1126/science.124.3220.493.b
fatcat:jyg7ug3d4fep5ks42jfzslhkzu
*Turing**machines*, and the fourth*with*the influence of unre- liable elements on*Turing*computability. ... The papers of the second part represent advances in the now well-known theory of*Turing**machines*, The first two papers deal*with*universal*Turing**machines*, the third*with*the question of inversion of func ...##
###
Automata Studies . C. E. Shannon and H. McCarthy. Princeton University Press, Princeton, N.J., 1956. 285 pp. $4

1956
*
Science
*

*Turing*

*machines*, and the fourth

*with*the influence of unre- liable elements on

*Turing*computability. ... The papers of the second part represent advances in the now well-known theory of

*Turing*

*machines*, The first two papers deal

*with*universal

*Turing*

*machines*, the third

*with*the question of inversion of func ...

##
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Synthesis of Succinct Systems
[article]

2012
*
arXiv
*
pre-print

., this is the standard way model checking problems are measured), research on synthesis has so far stayed

arXiv:1202.5449v2
fatcat:3wby2drkjrhhljfjeqpe3ezbqm
*with*measuring the system in terms of the explicit state space. ... We first non-deterministically guess an online*Turing**machine*M*with**with*|M| ∈ O(poly(|φ|)). ... A.2 Online*Turing**Machines*An online*Turing**machine*is a*Turing**machine**with*input and output that has additional restrictions on the transition function δ. ...##
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Page 1096 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

Summary: “Two

*Turing**machines*are described for a- computations of binary word reversals*with*as small as possible working zone. ... Summary: “We give an alternative proof of Bennett’s simulation of deterministic*Turing**machines*by reversible ones (*machines*whose configuration graph has out-degree and in-degree one)*with*a quadratic ...##
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Page 3875 of Mathematical Reviews Vol. , Issue 97F
[page]

1997
*
Mathematical Reviews
*

It is proved that a judgement

*with*a computing time complexity of O(n) on an off-line*Turing**machine*will need one of O(n?) if it is computed on a single-tape*Turing**machine*. ... Summary: “The difference in the computing time between the off- line*Turing**machine*and single-tape*Turing**machine*is investigated. ...##
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P is not equal to NP
[article]

2009
*
arXiv
*
pre-print

SAT is not in P, is true and provable in a simply consistent extension B' of a first order theory B of computing,

arXiv:0810.5056v2
fatcat:dk7kdfcwlvg7bi5sm4chpwdtiu
*with*a single finite axiom characterizing a universal*Turing**machine*. ... L ′ in In sentences (17) - (18) , there is an equivalence between*Turing**machine*i*with*input a and output u, and a universal*Turing**machine*computing output u*with*the concrete representations of : ... The beginning and end of the two-way tape itself are also marked*with*∅. 29 The universal*Turing**machine*in axiom B is also a logic program, i.e. for a*Turing**machine*i ∈ M*with*input a ∈ L and output ...
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