The Experts below are selected from a list of 15273 Experts worldwide ranked by ideXlab platform
Robert S Lubarsky - One of the best experts on this subject based on the ideXlab platform.
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An introduction to feedback Turing Computability
Journal of Logic and Computation, 2020Co-Authors: Nathanael L Ackerman, Cameron E Freer, Robert S LubarskyAbstract:Abstract Feedback Computability is computation with an oracle that contains the correct convergence/divergence information for all computations calling that same oracle. Here we study feedback Turing Computability, as well as feedback for some smaller classes of computation. We also examine some versions of parallelization of these notions.
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parallel feedback turing Computability
Foundations of Computer Science, 2016Co-Authors: Robert S LubarskyAbstract:In contrast to most kinds of Computability studied in mathematical logic, feedback Computability has a non-degenerate notion of parallelism. Here we study parallelism for the most basic kind of feedback, namely that of Turing Computability. We investigate several different possible definitions of parallelism in this context, with an eye toward specifying what is so computable. For the deterministic notions of parallelism identified we are successful in this analysis; for the non-deterministic notion, not completely.
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feedback turing Computability and turing Computability as feedback
Logic in Computer Science, 2015Co-Authors: Nathanael L Ackerman, Cameron E Freer, Robert S LubarskyAbstract:The notion of a feedback query is a natural generalization of choosing for an oracle the set of indices of halting computations. Notice that, in that setting, the computations being run are different from the computations in the oracle: the former can query an oracle, whereas the latter cannot. A feedback computation is one that can query an oracle, which itself contains the halting information about all feedback computations. Although this is self-referential, sense can be made of at least some such computations. This threatens, though, to obliterate the distinction between con- and divergence: before running a computation, a machine can ask the oracle whether that computation converges, and then run it if and only if the oracle says "yes." This would quickly lead to a diagonalization paradox, except that a new distinction is introduced, this time between freezing and non-freezing computations. The freezing computations are even more extreme than the divergent ones, in that they prevent the dovetailing on all computations into a single run. In this paper, we study feedback around Turing Computability. In one direction, we examine feedback Turing machines, and show that they provide exactly hyper arithmetic Computability. In the other direction, Turing Computability is itself feedback primitive recursion (at least, one version thereof). We also examine parallel feedback. Several different notions of parallelism in this context are identified. We show that parallel feedback Turing machines are strictly stronger than sequential feedback TMs, while in contrast parallel feedback p.r. Is the same as sequential feedback p.r.
Eli Gafni - One of the best experts on this subject based on the ideXlab platform.
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asynchronous Computability theorems for t resilient systems
International Symposium on Distributed Computing, 2016Co-Authors: Vikram Saraph, Maurice Herlihy, Eli GafniAbstract:A task is a distributed coordination problem where processes start with private inputs, communicate with one another, and then halt with private outputs. A protocol that solves a task is t-resilient if it tolerates halting failures by t or fewer processes. The t-resilient asynchronous Computability theorem stated here characterizes the tasks that have t-resilient protocols in a shared-memory model. This result generalizes the prior (wait-free) asynchronous Computability theorem of Herlihy and Shavit to a broader class of failure models, and requires introducing several novel concepts.
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a generalized asynchronous Computability theorem
Principles of Distributed Computing, 2014Co-Authors: Eli Gafni, Petr Kuznetsov, Ciprian ManolescuAbstract:We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task T and a model M, we provide topological conditions for T to be solvable in M. When applied to the wait-free model, our conditions result in the celebrated Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate the utility of our characterization, we consider a task that has been shown earlier to admit only a very complex t-resilient solution. In contrast, our generalized Computability theorem confirms its t-resilient solvability in a straightforward manner.
Keehang Kwon - One of the best experts on this subject based on the ideXlab platform.
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extending and automating basic probability theory with propositional Computability logic
arXiv: Artificial Intelligence, 2019Co-Authors: Keehang KwonAbstract:Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional Computability logic. Unlike other formalisms, Computability logic is built on the notion of events/games, which is central to probability theory. The probability theory based on CoL is therefore useful for {\it automating} uncertainty reasoning. We describe some basic properties of this new probability theory. We also discuss a novel isomorphism between the set operations and Computability logic operations.
Andrew E. M. Lewis - One of the best experts on this subject based on the ideXlab platform.
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The Journal of Symbolic Logic Volume 75,Number 1,March2010 THE IMPORTANCE OF Π01 CLASSES IN EFFECTIVE RANDOMNESS
2015Co-Authors: George Barmpalias, Andrew E. M. LewisAbstract:Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem. §1. Introduction. 1.1. Π01 classes in Computability and effective randomness. Many arguments in Computability theory and algorithmic randomness involve Π01 sets of reals and techniques specific to such sets in an essential way. Two major references to such arguments in Computability theory and in particular the degrees of unsolvability
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Infinite Time Turing Machines
Journal of Symbolic Logic, 2000Co-Authors: Joel David Hamkins, Andrew E. M. LewisAbstract:We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of Computability and decidability on the reals. Every set. for example, is decidable by such machines, and the semi-decidable sets form a portion of the sets. Our oracle concept leads to a notion of relative Computability for sets of reals and a rich degree structure, stratified by two natural jump operators.
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Infinite Time Turing Machines
arXiv: Logic, 1998Co-Authors: Joel David Hamkins, Andrew E. M. LewisAbstract:We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of Computability and decidability on the reals. The resulting Computability theory leads to a notion of computation on the reals and concepts of decidability and semi-decidability for sets of reals as well as individual reals. Every Pi^1_1 set, for example, is decidable by such machines, and the semi-decidable sets form a portion of the Delta^1_2 sets. Our oracle concept leads to a notion of relative Computability for reals and sets of reals and a rich degree structure, stratified by two natural jump operators.
Vikram Saraph - One of the best experts on this subject based on the ideXlab platform.
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asynchronous Computability theorems for t resilient systems
International Symposium on Distributed Computing, 2016Co-Authors: Vikram Saraph, Maurice Herlihy, Eli GafniAbstract:A task is a distributed coordination problem where processes start with private inputs, communicate with one another, and then halt with private outputs. A protocol that solves a task is t-resilient if it tolerates halting failures by t or fewer processes. The t-resilient asynchronous Computability theorem stated here characterizes the tasks that have t-resilient protocols in a shared-memory model. This result generalizes the prior (wait-free) asynchronous Computability theorem of Herlihy and Shavit to a broader class of failure models, and requires introducing several novel concepts.
