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Computability

About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.


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TL;DR: In this article, the authors consider the question whether there is an infinitary analogue of the Church-Turing-thesis and build a canonical model, called Idealized Agent Machines ($IAM$s) of this which will turn out to be equivalent in strength to the Ordinal Turing Machines defined by P. Koepke.
Abstract: We consider the question whether there is an infinitary analogue of the Church-Turing-thesis. To this end, we argue that there is an intuitive notion of transfinite computability and build a canonical model, called Idealized Agent Machines ($IAM$s) of this which will turn out to be equivalent in strength to the Ordinal Turing Machines defined by P. Koepke.

12 citations

Book ChapterDOI
03 Jun 2004
TL;DR: A general translation of term rewrite systems (TRS) to logic programs such that basic rewriting derivations become logic deductions and new classes of TRS that have nice properties like decidability of unification, regular sets of descendants or finite representations of R-unifiers are obtained.
Abstract: We present a general translation of term rewrite systems (TRS) to logic programs such that basic rewriting derivations become logic deductions. Certain TRS result in so-called cs-programs, which were originally studied in the context of constraint systems and tree tuple languages. By applying decidability and computability results of cs-programs we obtain new classes of TRS that have nice properties like decidability of unification, regular sets of descendants or finite representations of R-unifiers. Our findings generalize former results in the field of term rewriting.

12 citations

Journal ArticleDOI
22 Nov 2005
TL;DR: In this paper, the authors propose a reducibility having similar relationship to the Brzozowski's dot-depth hierarchy and some refinements, and prove some basic facts on the corresponding degree structure.
Abstract: Hierarchies considered in computability theory and in complexity theory are related to some reducibilities in the sense that levels of the hierarchies are downward closed and have complete sets. In this paper we propose a reducibility having similar relationship to the Brzozowski's dot-depth hierarchy and some its refinements. We prove some basic facts on the corresponding degree structure and discuss relationships of the reducibility to complexity theory (via the leaf-language approach).

12 citations

Proceedings ArticleDOI
28 Jun 2004
TL;DR: The achievements of students on the technical parts of this unit vs. its theoretical parts are compared and the correlation between achievements and two other factors are examined: the students' previous computer-related background (not necessarily computer science) and the level on which they studied mathematics.
Abstract: One of the units in the relatively new high school CS curriculum which is being implemented in Israel is a theoretical unit on computational models. It includes deterministic and non-deterministic finite automata, regular and non-regular languages, closure properties of regular languages, pushdown automata, closure properties of context free languages, Turing machines, the Church-Turing thesis and the halting problem. This paper focuses on part of a study we conducted dealing with the achievements of high school students studying this unit. Specifically, this paper compares the achievements of students on the technical parts of this unit vs. its theoretical parts. We also examine the correlation between achievements of students studying the Computational Models unit, and two other factors: The students' previous computer-related background (not necessarily computer science) and the level on which they studied mathematics.

11 citations

Book ChapterDOI
Kohtaro Tadaki1
03 Jan 2009
TL;DR: It is shown that the computability of each of all the thermodynamic quantities above gives the sufficient condition for T ⊆ (0,1) to be a fixed point on partial randomness.
Abstract: In our former work [K. Tadaki, Local Proceedings of CiE 2008,pp. 425---434, 2008], we developed a statistical mechanicalinterpretation of algorithmic information theory by introducing thenotion of thermodynamic quantities, such as free energyF (T ), energy E (T ), andstatistical mechanical entropy S (T ), into thetheory. We then discovered that, in the interpretation, thetemperature T equals to the partial randomness of thevalues of all these thermodynamic quantities, where the notion ofpartial randomness is a stronger representation of the compressionrate by program-size complexity. Furthermore, we showed that thissituation holds for the temperature itself as a thermodynamicquantity. Namely, the computability of the value of partitionfunction Z (T ) gives a sufficient condition forT ⊆ (0,1) to be a fixed point on partial randomness.In this paper, we show that the computability of each of all thethermodynamic quantities above gives the sufficient condition also.Moreover, we show that the computability of F (T )gives completely different fixed points from the computability ofZ (T ).

11 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202344
2022119
202189
202098
2019111
201897