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The laterality problem for non-erasing Turing machines on $\lbrace 0,1\rbrace $ is completely solved

Maurice Margenstern
1997 RAIRO - Theoretical Informatics and Applications  
-In aprevious work, [2], we defined a criterion which allowed to separate cases when ail non-erasing Turing machines on {0,1} have a decidable halting problem from cases where a universal non-erasing machine  ...  Applying a theorem which entails the just indicated frontier and analogous techniques based upon a qualitative study of the motions of the head of a Turing machine on its tape, another frontier resuit  ...  ACKNOWLEDGEMENTS The author thanks Serge Grigorieff for his constant attention and nis endless encouragings.  ... 
doi:10.1051/ita/1997310201591 fatcat:heoraxnqqngl3b7nhgwguk76hm

On quasi-unilateral universal Turing machines

Maurice Margenstern
2001 Theoretical Computer Science  
It is well known, that for unilateral machines, the halting problem is decidable.  ...  One of the machines is morever non-erasing, i.e. it does not erase any 1 written on the tape.  ...  EV NO950525 given by NATO Division of Scientiÿc A airs at the occasion of Liudmila Pavlotskaya's visit in June 1995, gave the best conditions for completing the ÿnal versions of the proof of Theorem 3.  ... 
doi:10.1016/s0304-3975(00)00114-6 fatcat:gvbjpb3n4jbr7jjjiy22a6ijkq

The complexity of small universal Turing machines: A survey

Damien Woods, Turlough Neary
2009 Theoretical Computer Science  
We also review a large number of old and new universal program size results, including new small universal Turing machines and new weakly, and semi-weakly, universal Turing machines.  ...  We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation.  ...  Acknowledgements We thank Olivier Bournez, Paola Bonizzoni and the organisers of Computability in Europe (CiE) 2007 for the invitation to this special issue.  ... 
doi:10.1016/j.tcs.2008.09.051 fatcat:uron5m7iezhxvelbf5cfl3ykq4

The Complexity of Small Universal Turing Machines: A Survey [chapter]

Turlough Neary, Damien Woods
2012 Lecture Notes in Computer Science  
We also review a large number of old and new universal program size results, including new small universal Turing machines and new weakly, and semi-weakly, universal Turing machines.  ...  We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation.  ...  Acknowledgements We thank Olivier Bournez, Paola Bonizzoni and the organisers of Computability in Europe (CiE) 2007 for the invitation to this special issue.  ... 
doi:10.1007/978-3-642-27660-6_32 fatcat:iqm5dzmdpnfvdkqc2cxm2m5gem

Verifying time complexity of Turing machines

David Gajser
2015 Theoretical Computer Science  
This is a tight bound on the order of growth for the function T because we prove that, for T(n)≥(n+1) and T(n)=Ω(n n), there exists no algorithm that would verify whether a given one-tape Turing machine  ...  In particular, we cannot verify whether a Turing machine runs in constant, polynomial or exponential time.  ...  Suppose a one-tape non-deterministic Turing machine M solves a problem L.  ... 
doi:10.1016/j.tcs.2015.07.028 fatcat:fvnwtvagpjgs7dhb46pqv6vbda

Small Weakly Universal Turing Machines [chapter]

Turlough Neary, Damien Woods
2009 Lecture Notes in Computer Science  
Minsky proved 2-tape nonwriting Turing machines were universal and showed 2-symbol non-erasing Turing machines simulate these non-writing machines.  ...  We say that f has frontier value of d for M 1 . Also, d may be described as a boundary between universality and non-universality in the following sense.  ...  To see this, compare the part of the Turing machine tape in bold with cells −7 to 0 of configuration c 1 in Figure 7 .2.1. We continue our simulation to give timestep c 1 ⊢ c 2 .  ... 
doi:10.1007/978-3-642-03409-1_24 fatcat:qm5hhofbxzbllbgbwlm32td3ny

Frontier between decidability and undecidability: a survey

Maurice Margenstern
2000 Theoretical Computer Science  
After recalling the deÿnition of decidability and universality, we ÿrst give a survey of results on the as exact as possible border betweeen a decidable problem and the corresponding undecidablity question  ...  We then go on with results more speciÿc to classical Turing machines, with a survey of results and a sketchy account on technics. We conclude by an illustration on simulating the 3x + 1 problem.  ...  The number of colours is a strong decidability criterion for non-erasing Turing machines on alphabet {0; 1} with 5 as a frontier value.  ... 
doi:10.1016/s0304-3975(99)00102-4 fatcat:qtfjyl7aunbjjlokq2tubukz5y

The Turing Machine Paradigm in Contemporary Computing [chapter]

Jan van Leeuwen, Jiří Wiedermann
2001 Mathematics Unlimited — 2001 and Beyond  
It is easily seen that Turing machines with advice can accept non-recursive languages. By way of illustration we show how to recognize the diagonal language of the halting problem using advice.  ...  There exists a Turing machine A with linearly bounded advice that accepts K and always halts. Proof. Define an advice function f as follows.  ... 
doi:10.1007/978-3-642-56478-9_59 fatcat:h2h73253r5fb3l2frsfofees6q

The machine as data: a computational view of emergence and definability

S. Barry Cooper
2015 Synthese  
And when the Þrst universal computers were built, a few years later, it was, again, not out of any special intention to implement universality.  ...  In 1936 Turing developed the definitive theory of universal classical computers.  ...  What we are left with is a sense of a more coherent and exciting universe, of which the computer does little more than scratch the surface.  ... 
doi:10.1007/s11229-015-0803-4 fatcat:4nkzyqyfhfh7dnnom3jd7l7n5q

On the boundaries of solvability and unsolvability in tag systems. Theoretical and Experimental Results

Liesbeth De Mol
2009 Electronic Proceedings in Theoretical Computer Science  
Several older and more recent results on the boundaries of solvability and unsolvability in tag systems are surveyed.  ...  The machine has 7 states and 4 symbols. Minsky's machine, however, has a defect: it erases its output before halting. Hence, it is not a truly universal machine.  ...  As a consequence, there is a significant gap between the size of the known universal tag systems and the tag systems known to have a decidable reachability problem.  ... 
doi:10.4204/eptcs.1.5 fatcat:24uwzlcbcfeu5chvcmdl2jkrke

Living Things Are Not (20th Century) Machines: Updating Mechanism Metaphors in Light of the Modern Science of Machine Behavior

Joshua Bongard, Michael Levin
2021 Frontiers in Ecology and Evolution  
We sketch a perspective that acknowledges the remarkable, unique aspects of life to help re-define key terms, and identify deep, essential features of concepts for a future in which sharp boundaries between  ...  Moving beyond contingent aspects of historical and current machines will enable conceptual tools that embrace inevitable advances in synthetic and hybrid bioengineering and computer science, toward a framework  ...  Veinott for their financial support, as well as the University of Vermont's Office of the Vice President for Research.  ... 
doi:10.3389/fevo.2021.650726 fatcat:hi6fq36rvffizcju23iwlj6axe

On the complex behavior of simple tag systems—An experimental approach

Liesbeth De Mol
2011 Theoretical Computer Science  
Special attention is given to the well-known example studied by Post with only 2 symbols and a deletion number v = 3.  ...  After a discussion of some of the main theoretical results on tag systems, several results from a computer-assisted and experimental study on tag systems are analyzed.  ...  Acknowledgement Part of this research was done during a research stay at the Boole centre for research in informatics, Cork university College.  ... 
doi:10.1016/j.tcs.2010.08.026 fatcat:g7yhicvzrjfptixzkqrep55ky4

Evolution Equations in Geometry [chapter]

Gerhard Huisken
2001 Mathematics Unlimited — 2001 and Beyond  
It is easily seen that Turing machines with advice can accept non-recursive languages. By way of illustration we show how to recognize the diagonal language of the halting problem using advice.  ...  There exists a Turing machine A with linearly bounded advice that accepts K and always halts. Proof. Define an advice function f as follows.  ... 
doi:10.1007/978-3-642-56478-9_30 fatcat:czfsrysgsfea7mqkewneviclea

On rules with existential variables: Walking the decidability line

Jean-François Baget, Michel Leclère, Marie-Laure Mugnier, Eric Salvat
2011 Artificial Intelligence  
The aim of this paper is to provide a clearer picture of the frontier between decidability and non-decidability of reasoning with these rules.  ...  We give a constructive definition of dependencies between rules and widen the landscape of decidable classes with conditions on rule dependencies and a mixed forward/backward chaining mechanism.  ...  Acknowledgements We thank Georg Gottlob for the reference to [37] , Michaël Thomazo for his careful reading of a previous version of this paper, as well as the anonymous reviewers for their relevant and  ... 
doi:10.1016/j.artint.2011.03.002 fatcat:pi5onanwwjhzdof67f7nshf6yi

Looking for Computers in the Biological Cell. After Twenty Years [chapter]

Gheorghe Păun
2016 Emergence, Complexity and Computation  
And, let us not forget, the life in the purity and signs world (a syntagma of Dan Barbilian-Ion Barbu, a Romanian mathematician and poet) This is the English version of the Reception Speech I have delivered  ...  Some ideas and some paragraphs of the text have appeared, in a preliminary version, in the paper Gh.  ...  ) can decide the halting problem.  ... 
doi:10.1007/978-3-319-33924-5_30 fatcat:5un6zuvwvfchbbqazd5h4eru3y
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