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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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01 Jan 1996
TL;DR: This study considers the complexity of the wait-free approximate agreement problem in an asynchronous shared memory comprised of only single-bit multi-writer multi-reader registers, and shows matching upper and lower bounds of $\Theta(s/\varepsilon)$ steps and shared registers.
Abstract: Agreement problems are central to the study of wait-free protocols for shared memory distributed systems. We examine two specific issues arising out of this study.
We consider the complexity of the wait-free approximate agreement problem in an asynchronous shared memory comprised of only single-bit multi-writer multi-reader registers. For real-valued inputs of magnitude at most s and a real-valued accuracy requirement $\varepsilon>0$ we show matching upper and lower bounds of $\Theta(\log(s/\varepsilon))$ steps and shared registers. For inputs drawn from any fixed finite range this is significantly better than the best possible algorithm for single-writer multi-reader registers, which, for n processes, requires $\Omega(\log\ n)$ steps. These results are used to show a separation between the wait-free single-writer multi-reader and wait-free multi-writer multi-reader models of computation.
The consensus hierarchy characterizes the strength of a shared object by its ability to solve the consensus problem in a wait-free manner. One important application of a hierarchy classifying the power of objects is to compare the power of systems offering different collections of objects. Ideally, a hierarchy should reduce the task of determining the strength of an architecture supporting shared memory distributed systems to the problem of determining the strength of each type of shared object supported by the architecture. Informally, a hierarchy that allows this is robust. Several variations of the consensus hierarchy have appeared in the literature, and it has been shown that all but one of them are not robust. The remaining hierarchy, named $h\sbsp{m}{r},$ has been the subject of considerable research. We show that, in a natural setting, the consensus hierarchy $h\sbsp{m}{r}$ is not robust.
10 citations
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TL;DR: The recognition problem for languages generated by pushdown store machines is related to compilation of programming languages because such languages exhibit many of the syntactic properties of algorithmic programming languages.
Abstract: This paper is concerned with the recognition of words which are contained in languages defined by pushdown store machines. Such languages exhibit many of the syntactic properties of algorithmic programming languages. Thus the recognition problem for languages generated by pushdown store machines is related to compilation of programming languages.
10 citations
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TL;DR: A construction due to Fouché in which a Brownian motion is constructed from an algorithmically random infinite binary sequence is examined, showing that although the construction is provably not computable in the sense of computable analysis, a lower bound for the rate of convergence is computable, making the construction layerwise computable.
Abstract: We examine a construction due to Fouche in which a Brownian motion is constructed from an algorithmically random infinite binary sequence. We show that although the construction is provably not computable in the sense of computable analysis, a lower bound for the rate of convergence is computable in any upper bound for the compressibilty of the sequence, making the construction layerwise computable.
10 citations
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TL;DR: A version of the magic sets technique for DFRP programs is designed, which ensures query equivalence under both brave and cautious reasoning, and it is shown that, if the input program is D FRP, then its magic-sets rewriting is guaranteed to be finitely ground.
Abstract: The support for function symbols in logic programming under answer set semantics allows us to overcome some modeling limitations of traditional Answer Set Programming (ASP) systems, such as the inability of handling infinite domains. On the other hand, admitting function symbols in ASP makes inference undecidable in the general case. Recently, the research community has been focusing on finding proper subclasses of programs with functions for which decidability of inference is guaranteed. The two major proposals, so far, are finitary programs and finitely-ground programs. These two proposals are somehow complementary: indeed, the former is conceived to allow decidable querying (by means of a top-down evaluation strategy), while the latter supports the computability of answer sets (by means of a bottom-up evaluation strategy). One of the main advantages of finitely-ground programs is that they can be “directly” evaluated by current ASP systems, which are based on a bottom-up computational model. However, there are also some interesting programs which are suitable for top-down query evaluation; but they do not fall in the class of finitely-ground programs.
In this paper, we focus on disjunctive finitely recursive positive (DFRP) programs. We design a version of the magic sets technique for DFRP programs, which ensures query equivalence under both brave and cautious reasoning. We show that, if the input program is DFRP, then its magic-sets rewriting is guaranteed to be finitely ground. Reasoning on DFRP programs turns out to be decidable; and we provide also an effective method that allows one to simply perform this reasoning by using the ASP system DLV.
10 citations
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08 Jul 2020TL;DR: It is revealed that logical problems used in most approaches are far more difficult than the verification problem; the only exception is the validity problem of first-order arithmetic with fixed-point operators.
Abstract: This paper studies the hardness of branching-time property verification of Turing-complete programming languages, as well as logical approaches to the verification problem. As these approaches reduce the verification problem to logical problems, e.g. the satisfiability problem of Horn clauses with certain extensions, it is natural to ask whether the logical problems are as hard as the verification problem or strictly harder. This paper reveals that logical problems used in most approaches are far more difficult than the verification problem; the only exception is the validity problem of first-order arithmetic with fixed-point operators. We also answers some other natural questions, for example, whether the extensions of Horn clauses are necessarily.
10 citations