On Turing Completeness, or Why We Are So Many

2017 ◽  
Author(s):  
Rammn Casares
Keyword(s):  
Turing Completeness

scholarly journals Parallel communicating grammar systems with context-free components are Turing complete for any communication model

2016 ◽  
Vol 8 (2) ◽  
pp. 113-170
Author(s):  
Mary Sarah Ruth Wilkin ◽  
Stefan D. Bruda
Keyword(s):  
Concurrent Systems ◽  
Communication Model ◽  
Broadcast Communication ◽  
Turing Completeness ◽  
One Step ◽  
Grammar Systems ◽  
Turing Complete ◽  
Context Free ◽  
Original Construction ◽  
Parallel Communicating Grammar Systems

Abstract Parallel Communicating Grammar Systems (PCGS) were introduced as a language-theoretic treatment of concurrent systems. A PCGS extends the concept of a grammar to a structure that consists of several grammars working in parallel, communicating with each other, and so contributing to the generation of strings. PCGS are usually more powerful than a single grammar of the same type; PCGS with context-free components (CF-PCGS) in particular were shown to be Turing complete. However, this result only holds when a specific type of communication (which we call broadcast communication, as opposed to one-step communication) is used. We expand the original construction that showed Turing completeness so that broadcast communication is eliminated at the expense of introducing a significant number of additional, helper component grammars. We thus show that CF-PCGS with one-step communication are also Turing complete. We introduce in the process several techniques that may be usable in other constructions and may be capable of removing broadcast communication in general.

scholarly journals Turing-completeness of asynchronous non-camouflage cellular automata

2020 ◽  
Vol 274 ◽  
pp. 104539 ◽  
Author(s):  
Tatsuya Yamashita ◽  
Teijiro Isokawa ◽  
Ferdinand Peper ◽  
Ibuki Kawamata ◽  
Masami Hagiya
Keyword(s):  
Cellular Automata ◽  
Turing Completeness

scholarly journals Turing-Completeness of Asynchronous Non-camouflage Cellular Automata

2017 ◽  
pp. 187-199 ◽  
Author(s):  
Tatsuya Yamashita ◽  
Teijiro Isokawa ◽  
Ferdinand Peper ◽  
Ibuki Kawamata ◽  
Masami Hagiya
Keyword(s):  
Cellular Automata ◽  
Turing Completeness

Convergence, continuity, recurrence and Turing completeness in dynamic epistemic logic1

2020 ◽  
Vol 30 (6) ◽  
pp. 1213-1238
Author(s):  
Dominik Klein ◽  
Rasmus K Rendsvig
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Model Transformations ◽  
Continuous Mappings ◽  
Turing Completeness ◽  
Action Model ◽  
Free Case ◽  
Finite Action ◽  
Action Models ◽  
Turing Complete

Abstract The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the Stone topology, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behaviour of said maps. Among the recurrence results, we show maps induced by finite action models may have uncountably many recurrent points, even when initiated on a finite input model. Several recurrence results draws on the class of action models being Turing complete, for which the paper provides proof in the postcondition-free case. As upper bounds, it is shown that either 1 atom, 3 agents and preconditions of modal depth 18 or 1 atom, 7 agents and preconditions of modal depth 3 suffice for Turing completeness.

scholarly journals BANISHING ROBUST TURING COMPLETENESS

1993 ◽  
Vol 04 (03) ◽  
pp. 245-265 ◽  
Author(s):  
LANE A. HEMASPAANDRA ◽  
SANJAY JAIN ◽  
NIKOLAI K. VERESHCHAGIN
Keyword(s):  
Open Questions ◽  
Turing Completeness ◽  
Complete Sets ◽  
Downward Closure ◽  
Turing Complete

This paper proves that “promise classes” are so fragilely structured that they do not robustly (i.e. with respect to all oracles) possess Turinghard sets even in classes far larger than themselves. In particular, this paper shows that FewP does not robustly possess Turing hard sets for UP∩coUP and IP∩coIP does not robustly possess Turing hard sets for ZPP. It follows that ZPP, R, coR, UP∩coUP, UP, FewP∩coFewP, FewP, and IP∩coIP do not robustly possess Turing complete sets. This both resolves open questions of whether promise classes lacking robust downward closure under Turing reductions (e.g., R, UP, FewP) might robustly have Turing complete sets, and extends the range of classes known not to robustly contain many-one complete sets.

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