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Turing Machines with Atoms

Mikolaj Bojanczyk, Bartek Klin, Slawomir Lasota, Szymon Torunczyk
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
We study 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.  ... 
doi:10.1109/lics.2013.24 dblp:conf/lics/BojanczykKLT13 fatcat:bntizruis5bezdfgmwuemw7jje

Turing machines with atoms, constraint satisfaction problems, and descriptive complexity

Bartek Klin, Sławomir Lasota, Joanna Ochremiak, Szymon Toruńczyk
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 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.  ... 
doi:10.1145/2603088.2603135 dblp:conf/csl/KlinLOT14 fatcat:whpzig7cnbhlzogjpkqpsuczbq

Super Turing-machines

B. Jack Copeland
1998 Complexity  
He described these as 'a new kind of 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.  ... 
doi:10.1002/(sici)1099-0526(199809/10)4:1<30::aid-cplx9>3.0.co;2-8 fatcat:gg4ioowwtvhktfh7pnj4ql7dhy

Degrees of Transducibility [chapter]

Jörg Endrullis, Jan Willem Klop, Aleksi Saarela, Markus Whiteland
2015 Lecture Notes in Computer Science  
As transformational devices, we focus here on 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  ... 
doi:10.1007/978-3-319-23660-5_1 fatcat:57hl6axxanbi7gqagwhifm5dru

Reactive Turing Machines with Infinite Alphabets [article]

Bas Luttik, Fei Yang
2017 arXiv   pre-print
The notion of Reactive 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.  ... 
arXiv:1610.06552v3 fatcat:l4yvkjifdvc27grzpry4iiewt4

Finitely unstable theories and computational complexity [article]

Tuomo Kauranne
2014 arXiv   pre-print
iff the 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.  ... 
arXiv:1410.4925v1 fatcat:opzk733isfcntgssmcepys4e7q

Quantum Speed‐up of Computations

Itamar Pitowsky
2002 Philosophy of Science  
Consequently, one can physically 'realize' a universal 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.  ... 
doi:10.1086/341843 fatcat:zf6rh63d4jgpzenyci2es63v4a

Atoms and Energy . H. W. S. Massey. Philosophical Library, New York, 1956. 174 pp. Illus. $4.75

R. D. Myers
1956 Science  
- tions defined by 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  ... 
doi:10.1126/science.124.3220.493-a fatcat:yw3j6sojnvbz7p5rh2u3mjv3i4

Atoms and Energy . H. W. S. Massey. Philosophical Library, New York, 1956. 174 pp. Illus. $4.75

R. D. Myers
1956 Science  
- tions defined by 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  ... 
doi:10.1126/science.124.3220.493.a fatcat:k4nob5guhzhi7asrc6ivcuu6n4

Automata Studies . C. E. Shannon and H. McCarthy. Princeton University Press, Princeton, N.J., 1956. 285 pp. $4

E. J. Cogan
1956 Science  
- tions defined by 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  ... 
doi:10.1126/science.124.3220.493.b fatcat:jyg7ug3d4fep5ks42jfzslhkzu

Automata Studies . C. E. Shannon and H. McCarthy. Princeton University Press, Princeton, N.J., 1956. 285 pp. $4

E. J. Cogan
1956 Science  
- tions defined by 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  ... 
doi:10.1126/science.124.3220.493-b fatcat:5erp7kixrzgyxkbosn6hpw7pje

Synthesis of Succinct Systems [article]

John Fearnley, Doron Peled, Sven Schewe
2012 arXiv   pre-print
., this is the standard way model checking problems are measured), research on synthesis has so far stayed 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.  ... 
arXiv:1202.5449v2 fatcat:3wby2drkjrhhljfjeqpe3ezbqm

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  ... 

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.  ... 

P is not equal to NP [article]

Sten-Ake Tarnlund
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, 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  ... 
arXiv:0810.5056v2 fatcat:dk7kdfcwlvg7bi5sm4chpwdtiu
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