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On the Decision Problem for TwoVariable FirstOrder Logic
, 1997
"... We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity ..."
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Cited by 54 (1 self)
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We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO² has the finitemodel property, which means that if an FO²sentence is satisfiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO²sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO²sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO² is NEXPTIMEcomplete.
A lambda calculus for quantum computation
 SIAM Journal of Computing
"... The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propos ..."
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Cited by 54 (1 self)
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The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lambda calculus suitable for expressing and reasoning about quantum algorithms. In this paper we develop a quantum lambda calculus as an alternative model of quantum computation, which combines some of the benefits of both the quantum Turing machine and the quantum circuit models. The calculus turns out to be closely related to the linear lambda calculi used in the study of Linear Logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.
Trivial Reals
"... Solovay showed that there are noncomputable reals ff such that H(ff _ n) 6 H(1n) + O(1), where H is prefixfree Kolmogorov complexity. Such Htrivial reals are interesting due to the connection between algorithmic complexity and effective randomness. We give a new, easier construction of an Htrivi ..."
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Cited by 54 (29 self)
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Solovay showed that there are noncomputable reals ff such that H(ff _ n) 6 H(1n) + O(1), where H is prefixfree Kolmogorov complexity. Such Htrivial reals are interesting due to the connection between algorithmic complexity and effective randomness. We give a new, easier construction of an Htrivial real. We also analyze various computabilitytheoretic properties of the Htrivial reals, showing for example that no Htrivial real can compute the halting problem. Therefore, our construction of an Htrivial computably enumerable set is an easy, injuryfree construction of an incomplete computably enumerable set. Finally, we relate the Htrivials to other classes of &quot;highly nonrandom &quot; reals that have been previously studied.
Returnoriented rootkits: Bypassing kernel code integrity protection mechanisms
 Proceedings of Usenix Security 2009. USENIX
, 2009
"... Protecting the kernel of an operating system against attacks, especially injection of malicious code, is an important factor for implementing secure operating systems. Several kernel integrity protection mechanism were proposed recently that all have a particular shortcoming: They cannot protect aga ..."
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Cited by 52 (1 self)
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Protecting the kernel of an operating system against attacks, especially injection of malicious code, is an important factor for implementing secure operating systems. Several kernel integrity protection mechanism were proposed recently that all have a particular shortcoming: They cannot protect against attacks in which the attacker reuses existing code within the kernel to perform malicious computations. In this paper, we present the design and implementation of a system that fully automates the process of constructing instruction sequences that can be used by an attacker for malicious computations. We evaluate the system on different commodity operating systems and show the portability and universality of our approach. Finally, we describe the implementation of a practical attack that can bypass existing kernel integrity protection mechanisms. 1
evolution and application of functional programming languages
 ACM Computing surveys
, 1989
"... The foundations of functional programming languages are examined from both historical and technical perspectives. Their evolution is traced through several critical periods: early work on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and modern functional languages such as Miranda ’ ..."
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Cited by 51 (0 self)
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The foundations of functional programming languages are examined from both historical and technical perspectives. Their evolution is traced through several critical periods: early work on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and modern functional languages such as Miranda ’ and Haskell. The fundamental premises on which the functional programming methodology stands are critically analyzed with respect to philosophical, theoretical, and pragmatic concerns. Particular attention is paid to the main features that characterize modern functional languages: higherorder functions, lazy evaluation, equations and pattern matching, strong static typing and type inference, and data abstraction. In addition, current research areassuch as parallelism, nondeterminism, input/output, and stateoriented computationsare examined with the goal of predicting the future development and application of functional languages.
PCF extended with real numbers
, 1996
"... We extend the programming language PCF with a type for (total and partial) real numbers. By a partial real number we mean an element of a cpo of intervals, whose subspace of maximal elements (singlepoint intervals) is homeomorphic to the Euclidean real line. We show that partial real numbers can be ..."
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Cited by 49 (15 self)
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We extend the programming language PCF with a type for (total and partial) real numbers. By a partial real number we mean an element of a cpo of intervals, whose subspace of maximal elements (singlepoint intervals) is homeomorphic to the Euclidean real line. We show that partial real numbers can be considered as “continuous words”. Concatenation of continuous words corresponds to refinement of partial information. The usual basic operations cons, head and tail used to explicitly or recursively define functions on words generalize to partial real numbers. We use this fact to give an operational semantics to the above referred extension of PCF. We prove that the operational semantics is sound and complete with respect to the denotational semantics. A program of real number type evaluates to a headnormal form iff its value is different from ⊥; if its value is different from ⊥ then it successively evaluates to headnormal forms giving better and better partial results converging to its value.
Optimized Rapid Prototyping for RealTime Embedded Heterogeneous Multiprocessors
, 1999
"... This paper presents an enhancement of our "Algorithm Architecture Adequation" (AAA) prototyping methodology which allows to rapidly develop and optimize the implementation of a reactive realtime dataflow algorithm on a embedded heterogeneous multiprocessor architecture, predict its realt ..."
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Cited by 46 (11 self)
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This paper presents an enhancement of our "Algorithm Architecture Adequation" (AAA) prototyping methodology which allows to rapidly develop and optimize the implementation of a reactive realtime dataflow algorithm on a embedded heterogeneous multiprocessor architecture, predict its realtime behavior and automatically generate the corresponding distributed and optimized static executive. It describes a new optimization heuristic able to support heterogeneous architectures and takes into account accurately interprocessor communications, which are usually neglected but may reduce dramatically multiprocessor performances. 1 Introduction The increasing complexity of signal, image and control processing algorithms in embedded applications, requires high computational power to satisfy realtime constraints. This power can be achieved by parallel multiprocessors which are often heterogeneous in embedded system: they are made of different types of processors interconnected by different typ...
A DomainTheoretic Approach to Computability on the Real Line
, 1997
"... In recent years, there has been a considerable amount of work on using continuous domains in real analysis. Most notably are the development of the generalized Riemann integral with applications in fractal geometry, several extensions of the programming language PCF with a real number data type, and ..."
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Cited by 44 (10 self)
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In recent years, there has been a considerable amount of work on using continuous domains in real analysis. Most notably are the development of the generalized Riemann integral with applications in fractal geometry, several extensions of the programming language PCF with a real number data type, and a framework and an implementation of a package for exact real number arithmetic. Based on recursion theory we present here a precise and direct formulation of effective representation of real numbers by continuous domains, which is equivalent to the representation of real numbers by algebraic domains as in the work of StoltenbergHansen and Tucker. We use basic ingredients of an effective theory of continuous domains to spell out notions of computability for the reals and for functions on the real line. We prove directly that our approach is equivalent to the established Turingmachine based approach which dates back to Grzegorczyk and Lacombe, is used by PourEl & Richards in their found...
QuantumInspired Computing
, 1995
"... The paper identifies and demonstrates the feasibility of a novel computational paradigm which is inspired by the principles of quantum mechanics and quantum computing. A brief history of quantum computing and basic exposition of quantum mechanics are provided, followed by a detailed description of S ..."
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Cited by 44 (6 self)
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The paper identifies and demonstrates the feasibility of a novel computational paradigm which is inspired by the principles of quantum mechanics and quantum computing. A brief history of quantum computing and basic exposition of quantum mechanics are provided, followed by a detailed description of Shor's quantum `algorithm' for factoring very large numbers. An extension to Shor's method is described, and this leads to two further applications of `quantuminspired' methods: sorting, and the 15puzzle. In all cases, quantuminspired methods require the use of `classical' methods to determine whether the candidate answers provided by the quantuminspired methods are correct. Finally, some basic methodological principles and guidelines are provided for quantuminspired computing. The aim is not to provide a formal exposition of quantuminspired computing but to identify its novelty and potential use in tackling NPhard problems. 1 Introduction It has been estimated that every two years ...