Small universal Turing machines

Rogozhin, Yurii

doi:10.1016/s0304-3975(96)00077-1

Cited by 183 publications

(124 citation statements)

References 3 publications

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“…: universal, direct simulation, O(t 2 ), [65] : universal, 2-tag simulation, O(t 4 log 2 t), [4,27,91] : universal, bi-tag simulation, O(t 6 ), [69] : semi-weakly universal, direct simulation, O(t 2 ), [105] : semi-weakly universal, cyclic-tag simulation, O(t 4 log 2 t), [111] : weakly universal, Rule 110 simulation, O(t 4 log 2 t), [68] universal non-universal Despite the existence of these efficient O(t 2 ) simulators, it still remained the case that the smallest universal machines were exponentially slow. However, we have recently shown that the smallest machines are in fact efficient simulators of Turing machines, by showing that 2-tag systems are efficient [108].…”

Section: Time and Size Efficiency Of Universal Machinesmentioning

confidence: 99%

“…The 5-symbol machine improves on the 5-symbol machine of Rogozhin [91] by one transition rule. The remainder of these machines improve on the 2-and 4-symbol machines of Baiocchi [4], and the 3-symbol machine of Rogozhin [91]. These small machines simulate Turing machines in polynomial time O(t 6 ) and are illustrated as triangles in Figure 1.…”

Section: Time and Size Efficiency Of Universal Machinesmentioning

confidence: 99%

“…Rogozhin [88] extended Minsky's technique of 2-tag simulation and found small machines with a number of state-symbol pairs. Subsequently, some of Rogozhin's machines were reduced in size or improved by Robinson [86,91], Kudlek and Rogozhin [27], and Baiocchi [4]. All of the smallest known 2-tag simulators are plotted as circles in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

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The Complexity of Small Universal Turing Machines: A Survey

Neary

Woods

2012

SOFSEM 2012: Theory and Practice of Computer Science

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Abstract. We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. In addition, another related result shows that Rule 110, a well-known elementary cellular automaton, is efficiently universal. We also discuss some old and new universal program size results, including the smallest known universal Turing machines. We finish the survey with results on generalised and restricted Turing machine models including machines with a periodic background on the tape (instead of a blank symbol), multiple tapes, multiple dimensions, and machines that never write to their tape. We then discuss some ideas for future work.

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Section: Time and Size Efficiency Of Universal Machinesmentioning

confidence: 99%

Section: Time and Size Efficiency Of Universal Machinesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Complexity of Small Universal Turing Machines: A Survey

Neary

Woods

2012

SOFSEM 2012: Theory and Practice of Computer Science

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“…If we use the small universal Turing machine presented in [Rog96], having 4 states and 6 symbols, we obtain the following theorem.…”

Section: Definition 21mentioning

confidence: 99%

“…The idea to prove this theorem is to simulate with a set of polynomial ODEs Rogozhin's small universal Turing machine [Rog96]. We can obtain a set of PIVPs simulating this Turing machine as described by Theorem 13, Proposition 14, and Corollary 15.…”

Section: Definition 21mentioning

confidence: 99%

Computational bounds on polynomial differential equations

Graça

Buescu

Campagnolo

2009

Applied Mathematics and Computation

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In this paper we study from a computational perspective some properties of the solutions of polynomial ordinary differential equations.We consider elementary (in the sense of Analysis) discrete-time dynamical systems satisfying certain criteria of robustness. We show that those systems can be simulated with elementary and robust continuous-time dynamical systems which can be expanded into fully polynomial ordinary differential equations with coefficients in Q[π]. This sets a computational lower bound on polynomial ODEs since the former class is large enough to include the dynamics of arbitrary Turing machines.We also apply the previous methods to show that the problem of determining whether the maximal interval of definition of an initial-value problem defined with polynomial ODEs is bounded or not is in general undecidable, even if the parameters of the system are computable and comparable and if the degree of the corresponding polynomial is at most 56.Combined with earlier results on the computability of solutions of polynomial ODEs, one can conclude that there is from a computational point of view a close connection between these systems and Turing machines.

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Finite state machine for cloud forensic readiness as a service (CFRaaS) events

Kebande

Choo

2021

Security and Privacy

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The importance of demonstrating the correctness of forensic analysis tools and automated incident management tools reinforces the need for a finite state machine (FSM) engine that can generate automated forensic processes. Hence, in this paper, we present an event-based FSM representation for Cloud Forensic Readiness as a Service (CFRaaS), where we also show how the FSM's predetermined states and transitions could be used to formulate an automated forensic process and generate a hypothesis for litigation purposes. Specifically, this proposition comprises a two-step level CFRaaS-FSM with possible transitions and states. This representation is useful because it can alert digital forensic investigators on how to deduce current and next state of attacks based on transitions and current states.

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Small universal Turing machines

Cited by 183 publications

References 3 publications

The Complexity of Small Universal Turing Machines: A Survey

The Complexity of Small Universal Turing Machines: A Survey

Computational bounds on polynomial differential equations

Finite state machine for cloud forensic readiness as a service (CFRaaS) events

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