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Turing Automata and Graph Machines

Miklós Bartha
2010 Electronic Proceedings in Theoretical Computer Science  
Turing automata and Turing graph machines are defined by generalizing the classical Turing machine concept, so that the collection of such machines becomes an indexed monoidal algebra.  ...  On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular  ...  Turing automata and Turing graph machines As an important example of indexed monoidal algebras, in this section we introduce the algebra of Turing automata and Turing graph machines.  ... 
doi:10.4204/eptcs.26.3 fatcat:vpory26l4bdzbdueqzbrqtj7f4

Turing Machines on Graphs and Inescapable Groups [article]

Aubrey da Cunha
2010 arXiv   pre-print
We present a generalization of standard Turing machines based on allowing unusual tapes.  ...  The definitions give rise to a number of questions about computable paths inside Cayley graphs of finitely generated groups, and several of these questions are answered.  ...  Power of Turing Machines on Cayley Graphs.  ... 
arXiv:1005.2636v1 fatcat:o2nox5vjafexfoqrt4mtflmw2y

On the transition graphs of turing machines

Didier Caucal
2003 Theoretical Computer Science  
Finally we show that this family is also the set of graphs recognized by (unlabelled) Turing machines with labelled ÿnal states, and even if we restrict to deterministic Turing machines.  ...  As for pushdown automata, we consider labelled Turing machines with -rules.  ...  The transition graphs of labelled Turing machines are the computation graphs of unlabelled Turing machines. Theorem 4.8.  ... 
doi:10.1016/s0304-3975(02)00655-2 fatcat:2h6kjdmuajharcytgrbtwj232e

On the Transition Graphs of Turing Machines [chapter]

Didier Caucal
2001 Lecture Notes in Computer Science  
Finally we show that this family is also the set of graphs recognized by (unlabelled) Turing machines with labelled nal states, and even if we restrict to deterministic Turing machines. caucal@irisa.fr  ...  As for pushdown automata, we consider labelled Turing machines with -rules.  ...  The transition graphs of labelled Turing machines are the computation graphs of unlabelled Turing machines.  ... 
doi:10.1007/3-540-45132-3_11 fatcat:fdoext5q4rhfznqwepwceus344

On the computability of graph Turing machines [article]

Nathanael Ackerman, Cameron Freer
2017 arXiv   pre-print
time and linear space by a graph Turing machine whose underlying graph has finite degree.  ...  We consider graph Turing machines, a model of parallel computation on a graph, in which each vertex is only capable of performing one of a finite number of operations.  ...  Ordinary Turing machines We begin by showing how to simulate an ordinary Turing machine by a graph Turing machine.  ... 
arXiv:1703.09406v1 fatcat:hct5pwerv5ghvotmotfmufkacy

On Extremal Graph Theory, Explicit Algebraic Constructions of Extremal Graphs and Corresponding Turing Encryption Machines [chapter]

Vasyl Ustimenko, Urszula Romańczuk
2013 Studies in Computational Intelligence  
In terms of Finite Automata Theory Turing machine is an infinite sequence of directed graphs with colours on arrows.  ...  The explicite constructions of simple and directed graphs of large girth (or large cycle indicator) corresponds to efficient encryption of Turing machines.  ...  Turing machine with Q = K.  ... 
doi:10.1007/978-3-642-29694-9_11 fatcat:t22qvy6blrdgzes7o74r752wce

On nontrivial separators for k-page graphs and simulations by nondeterministic one-tape Turing machines

Z Galil, R Kannan, E Szemeredi
1986 Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86  
-There is a language L recognizable in real time by a two-tape nondeterministic Turing machine, but every on-line one-tape nondeterministic Turing machine that recognizes L requires 0.  ...  Statement 2: A one-tape nondeterministic Turing machine can simulate a two-tape machine in subquadratic time. ~one of the statements is known to be true or false at present.  ...  They state properties of graphs and they are proved via a detour through Turing machines. All of them probably have direct proofs. Corollary 5.  ... 
doi:10.1145/12130.12135 dblp:conf/stoc/GalilKS86 fatcat:bgvmrnlvqjbercxepmmca44ezu

On nontrivial separators for k-page graphs and simulations by nondeterministic one-tape turing machines

Zvi Galil, Ravi Kannan, Endre Szemerédi
1989 Journal of computer and system sciences (Print)  
A one-tape nondeterministic Turing machine can simulate a two-tape machine in subquadratic time. None of the statements is known to be true or false at present.  ...  Using the equivalence we prove an almost linear lower bound for the size of separators for 3-pushdown graphs and an almost quadratic lower bound for simulating two-tape nondeterministic Turing machines  ...  Computation graphs of Turing machines are k-pd graphs, where k depends on the number of tapes of the Turing machine. This has been the reason for substantial interest in such graphs.  ... 
doi:10.1016/0022-0000(89)90036-6 fatcat:joloongagndvfihryhkld3adke

Godel, Turing, and K-graph machines

Sieg, John Byrnes
2018
Letter machines are easily seen to be K-graph machines and, that is the main technical result in our [1996], K-graph machines can be simulated by letter machines.  ...  In triangular terms, K-graph machines take the place of string machines.  ... 
doi:10.1184/r1/6491915.v1 fatcat:o4ky47yjrnfylezsatctt6pa6e

Storage Capacity of Labeled Graphs [chapter]

Dana Angluin, James Aspnes, Rida A. Bazzi, Jiang Chen, David Eisenstat, Goran Konjevod
2010 Lecture Notes in Computer Science  
More interesting is the effective capacity of members of some class of graphs, the number of states distinguishable by a Turing machine that uses the labeled graph itself in place of the usual linear tape  ...  We show that the effective capacity equals the information-theoretic capacity up to constant factors for trees, random graphs with polynomial edge probabilities, and bounded-degree graphs.  ...  Fix a graph Turing machine, and suppose it is used to simulate a standard Turing machine.  ... 
doi:10.1007/978-3-642-16023-3_44 fatcat:6cvcphjurfcqzjnxh4zrvfozky

Effective storage capacity of labeled graphs

Dana Angluin, James Aspnes, Rida A. Bazzi, Jiang Chen, David Eisenstat, Goran Konjevod
2014 Information and Computation  
Specifically, we are interested in the effective capacity of members of some class of graphs, the number of states distinguishable by a Turing machine that uses the labeled graph itself in place of the  ...  It equals the information-theoretic capacity of the graph up to constant factors for trees, random graphs with polynomial edge probabilities, and bounded-degree graphs.  ...  Graph Turing machines In this section, we define formally our notion of a graph Turing machine.  ... 
doi:10.1016/j.ic.2013.11.004 fatcat:fmnemau52raxbcqrihddkwtzx4

Graph splicing systems

Rahul Santhanam, Kamala Krithivasan
2006 Discrete Applied Mathematics  
In this paper, extended graph splicing systems are defined.  ...  It is shown that when strings are represented as linear graphs, any recursively enumerable set can be generated by an extended graph splicing system.  ...  Then we make use of the property that, for each Turing machine M, there exists a Turing machine M R such that w ∈ L(M) iff w R ∈ L(M R ).  ... 
doi:10.1016/j.dam.2005.12.005 fatcat:gjpjs6m2kfgorirvannqtao65q

On the Problem of Undirected st-connectivity [article]

Shilun Li, Alex Lee
2022 arXiv   pre-print
Finally, our paper also shows that undirected st-connectivity is within the L complexity class, problems solvable by deterministic Turing machines in logarithmic space.  ...  ., it is known that undirected st-connectivity is within the RL complexity class, problems solvable by randomized (probabilistic) Turing machines with one-sided error in logarithmic space and polynomial  ...  We note that our definition of Turing machine is equivalent to that of a standard Turing machine.  ... 
arXiv:2203.09728v1 fatcat:tp6nthsvovgrbdxassv3uwwpai

Unambiguous Catalytic Computation

Chetan Gupta, Rahul Jain, Vimal Raj Sharma, Raghunath Tewari, Michael Wagner
2019 Foundations of Software Technology and Theoretical Computer Science  
In this paper, we define the notion of unambiguous catalytic Turing machine and prove that under a standard derandomization assumption, the class of problems solved by an unambiguous catalytic Turing machine  ...  The catalytic Turing machine is a model of computation defined by Buhrman, Cleve, Koucký, Loff, and Speelman (STOC 2014).  ...  Analogous to the standard Turing machine, an unambiguous catalytic Turing machine is a nondeterministic catalytic Turing machine which has at most one accepting path on each input.  ... 
doi:10.4230/lipics.fsttcs.2019.16 dblp:conf/fsttcs/GuptaJST19 fatcat:xerymmqwifh4jbqqgijmc7yhc4

Reversible simulation of space-bounded computations

P Crescenzi
1995 Theoretical Computer Science  
Almmet We give an alternative proof of Bennett's simulation of deterministic "luring machines by reversible ones (machines whose configuration graph has out-degree and in-degree one) with a quadratic loss  ...  More importantly, our proof extends thi~ result to nondetermin~ic Turing  ...  It is easy to verity that the rcacbability problem for graphs with in-degree and out-degree at most one is solvable in thne O(n) and space O0ogn) by a reversible Turing machine.  ... 
doi:10.1016/0304-3975(95)80017-4 fatcat:dw7k3r6y2jbzznzmr256lybwae
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