A Universal Reversible Turing Machine

Morita, Kenichi; Yamaguchi, Yoshikazu

doi:10.1007/978-3-540-74593-8_8

Cited by 39 publications

(36 citation statements)

References 9 publications

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“…Following Morita [8], a Turing machine (TM) M is a tuple (Q, Σ, δ), where Q is a finite set of states, Σ is a finite set of symbols and δ ⊆ Q × Σ × Σ × Q ∪ Q × {/} × {−1, 0, +1} × Q is the writing/moving relation of the machine. The machine works on a tape, usually bi-infinite, full of symbols from Σ.…”

Section: Turing Machinementioning

confidence: 99%

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Undecidability of the Surjectivity of the Subshift Associated to a Turing Machine

Torres

Ollinger

Gajardo

2013

Reversible Computation

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Section: Turing Machinementioning

confidence: 99%

“…A Turing machine written in quadruples is backward deterministic (as seen in [8]) if and only if for any two different quadruples (q, s, s ′ , q ′ ) and (q ′′ , s ′′ , s ′′′ , q ′ ) in δ, it holds:…”

Section: Backward Deterministic Turing Machine a Turing Machine M Ismentioning

confidence: 99%

Undecidability of the Surjectivity of the Subshift Associated to a Turing Machine

Torres

Ollinger

Gajardo

2013

Reversible Computation

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“…The definition of a TM is mostly from [13]. A one-tape two-symbol TM is a system defined by M = (Q, Σ, q 0 , q m−1 , R), where Q = {q 0 , q 1 , .…”

Section: Transformation From Tms To Cast Puzzlesmentioning

confidence: 99%

NP-Hard and k-EXPSPACE-Hard Cast Puzzles

Iwamoto

Sasaki

Nishio

et al. 2010

IEICE Trans. Inf. & Syst.

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SUMMARYA disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A cast puzzle is a type of disentanglement puzzle, where each piece is a zinc die-casting alloy. In this paper, we consider the generalized cast puzzle problem whose input is the layout of a finite number of pieces (polyhedrons) in the 3-dimensional Euclidean space. For every integer k ≥ 0, we present a polynomial-time transformation from an arbitrary k-exponential-space Turing machine M and its input x to a cast puzzle c 1 of size k-exponential in |x| such that M accepts x if and only if c 1 is solvable. Here, the layout of c 1 is encoded as a string of length polynomial (even if c 1 has size k-exponential). Therefore, the cast puzzle problem of size k-exponential is k-EXPSPACE-hard for every integer k ≥ 0. We also present a polynomial-time transformation from an arbitrary instance f of the SAT problem to a cast puzzle c 2 such that f is satisfiable if and only if c 2 is solvable.

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“…They have been simplified in terms of the numbers of tapes, symbols, and states, as well as in a reversible setting [8], [9].…”

Section: Introductionmentioning

confidence: 99%

A Minimalist's Reversible While Language

Glück

Yokoyama

2017

IEICE Trans. Inf. & Syst.

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SUMMARY The paper presents a small reversible language R-CORE, a structured imperative programming language with symbolic tree-structured data (S-expressions). The language is reduced to the core of a reversible language, with a single command for reversibly updating the store, a single reversible control-flow operator, a limited number of variables, and data with a single atom and a single constructor. Despite its extreme simplicity, the language is reversibly universal, which means that it is as powerful as any reversible language can be, while it is linear-time self-interpretable, and it allows reversible programming with dynamic data structures. The four-line program inverter for R-CORE is among the shortest existing program inverters, which demonstrates the conciseness of the language. The translator to R-CORE, which is used to show the formal properties of the language, is clean and modular, and it may serve as a model for related reversible translation problems. The goal is to provide a language that is sufficiently concise for theoretical investigations. Owing to its simplicity, the language may also be used for educational purposes. key words: reversible programming language, reversible self-interpreter, while language, translation, program inversion

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A Universal Reversible Turing Machine

Cited by 39 publications

References 9 publications

Undecidability of the Surjectivity of the Subshift Associated to a Turing Machine

Undecidability of the Surjectivity of the Subshift Associated to a Turing Machine

NP-Hard and k-EXPSPACE-Hard Cast Puzzles

A Minimalist's Reversible While Language

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