1,571 research outputs found

    Instruction sequences with dynamically instantiated instructions

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    We study sequential programs that are instruction sequences with dynamically instantiated instructions. We define the meaning of such programs in two different ways. In either case, we give a translation by which each program with dynamically instantiated instructions is turned into a program without them that exhibits on execution the same behaviour by interaction with some service. The complexity of the translations differ considerably, whereas the services concerned are equally simple. However, the service concerned in the case of the simpler translation is far more powerful than the service concerned in the other case.Comment: 25 pages; phrasing improve

    The parameterized space complexity of model-checking bounded variable first-order logic

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    The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-checking problem for queries with a bounded number of variables. For each bound on the quantifier alternation rank the problem becomes complete for the corresponding level of what we call the tree hierarchy, a hierarchy of parameterized complexity classes defined via space bounded alternating machines between parameterized logarithmic space and fixed-parameter tractable time. We observe that a parameterized logarithmic space model-checker for existential bounded variable queries would allow to improve Savitch's classical simulation of nondeterministic logarithmic space in deterministic space O(log2n)O(\log^2n). Further, we define a highly space efficient model-checker for queries with a bounded number of variables and bounded quantifier alternation rank. We study its optimality under the assumption that Savitch's Theorem is optimal

    Termination proofs by multiset path orderings imply primitive recursive derivation lengths

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    AbstractIt is shown that a termination proof for a term-rewriting system using multiset path orderings (i.e. recursive path orderings with multiset status only) yields a primitive recursive bound on the length of derivations, measured in the size of the starting term, confirming a conjecture of Plaisted (1978). This result holds for a great variety of path orderings, including path of subterms ordering, recursive decomposition ordering, and the path ordering of Kapur (1985) if lexicographic status is not incorporated. The result is essentially optimal as such derivation lengths can be found in each level of the Grzegorczyk hierarchy, even for string-rewriting systems

    Parameterized Uniform Complexity in Numerics: from Smooth to Analytic, from NP-hard to Polytime

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    The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are known to map (even high-order differentiable) polynomial-time computable functions to instances which are `hard' for classical complexity classes NP, #P, and CH; but, restricted to analytic functions, map polynomial-time computable ones to polynomial-time computable ones -- non-uniformly! We investigate the uniform parameterized complexity of the above operators in the setting of Weihrauch's TTE and its second-order extension due to Kawamura&Cook (2010). That is, we explore which (both continuous and discrete, first and second order) information and parameters on some given f is sufficient to obtain similar data on Max(f) and int(f); and within what running time, in terms of these parameters and the guaranteed output precision 2^(-n). It turns out that Gevrey's hierarchy of functions climbing from analytic to smooth corresponds to the computational complexity of maximization growing from polytime to NP-hard. Proof techniques involve mainly the Theory of (discrete) Computation, Hard Analysis, and Information-Based Complexity

    Circuit design tool. User's manual, revision 2

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    The CAM chip design was produced in a UNIX software environment using a design tool that supports definition of digital electronic modules, composition of these modules into higher level circuits, and event-driven simulation of these circuits. Our design tool provides an interface whose goals include straightforward but flexible primitive module definition and circuit composition, efficient simulation, and a debugging environment that facilitates design verification and alteration. The tool provides a set of primitive modules which can be composed into higher level circuits. Each module is a C-language subroutine that uses a set of interface protocols understood by the design tool. Primitives can be altered simply by recoding their C-code image; in addition new primitives can be added allowing higher level circuits to be described in C-code rather than as a composition of primitive modules--this feature can greatly enhance the speed of simulation

    Fix Your Types

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    When using existing ACL2 datatype frameworks, many theorems require type hypotheses. These hypotheses slow down the theorem prover, are tedious to write, and are easy to forget. We describe a principled approach to types that provides strong type safety and execution efficiency while avoiding type hypotheses, and we present a library that automates this approach. Using this approach, types help you catch programming errors and then get out of the way of theorem proving.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

    Capabilities and Limitations of Infinite-Time Computation

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    The relatively new field of infinitary computability strives to characterize thecapabilities and limitations of infinite-time computation; that is, computations ofpotentially transfinite length. Throughout our work, we focus on the prototypicalmodel of infinitary computation: Hamkins and Lewis\u27 infinite-time Turing machine(ITTM), which generalizes the classical Turing machine model in a naturalway.This dissertation adopts a novel approach to this study: whereas most of theliterature, starting with Hamkins and Lewis\u27 debut of the ITTM model, pursuesset-theoretic questions using a set-theoretic approach, we employ arguments thatare truly computational in character. Indeed, we fully utilize analogues of classicalresults from finitary computability, such as the s-m-n Theorem and existence ofuniversal machines, and for the most part, judiciously restrict our attention to theclassical setting of computations over the natural numbers.In Chapter 2 of this dissertation, we state, and derive, as necessary, the aforementionedanalogues of the classical results, as well as some useful constructs for ITTM programming. With this due paid, the subsequent work in Chapters 3 and 4 requires little in the way of programming, and that programming which is required in Chapter 5 is dramatically streamlined. In Chapter 3, we formulate two analogues of one of Rado\u27s busy beaver functions from classical computability, and show, in analogy with Rado\u27s results, that they grow faster than a wide class of infinite-time computable functions. Chapter 4 is tasked with developing a system of ordinal notations via a natural approach involving infinite-time computation, as well as an associated fast-growing hierarchy of functions over the natural numbers. We then demonstrate that the busy beaver functions from Chapter 3 grow faster than the functions which appear in a significant portion of this hierarchy. Finally, we debut, in Chapter 5, two enhancements of the ITTM model whichcan self-modify certain aspects of their underlying software and hardware mid-computation, and show the somewhat surprising fact that, under some reasonableassumptions, these new models of infinitary computation compute precisely thesame functions as the original ITTM model
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