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Logical Depth and Physical Complexity
 THE UNIVERSAL TURING MACHINE: A HALFCENTURY SURVEY
, 1988
"... Some mathematical and natural objects (a random sequence, a sequence of zeros, a perfect crystal, a gas) are intuitively trivial, while others (e.g. the human body, the digits of #) contain internal evidence of a nontrivial causal history. We formalize this ..."
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Cited by 48 (0 self)
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Some mathematical and natural objects (a random sequence, a sequence of zeros, a perfect crystal, a gas) are intuitively trivial, while others (e.g. the human body, the digits of #) contain internal evidence of a nontrivial causal history. We formalize this
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 48 (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.
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 47 (14 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.
Routines and other recurring action patterns of organizations: Contemporary research issues
 Industrial and Corporate Change
, 1996
"... This paper reports and extends discussions carried out during a workshop held at the Santa Fe Institute in August 1995 by the authors. It treats eight major topics: (i) the importance of carefully examining research on routine, (it) the concept of 'action patterns ' in general and in terms of routin ..."
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Cited by 45 (10 self)
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This paper reports and extends discussions carried out during a workshop held at the Santa Fe Institute in August 1995 by the authors. It treats eight major topics: (i) the importance of carefully examining research on routine, (it) the concept of 'action patterns ' in general and in terms of routine, (Hi) the useful categorization of routines and other recurring patterns, (iv) the research implications of recent cognitive results, (v) the relation of evolution to action patterns, (vi) the contributions of simulation modeling for theory in this area, (vii) examples of various approaches to empirical jj; research that reveal key problems, and (viii) a possible definition of 'routine'. An m extended appendix by Massimo Egidi provides a lexicon of synonyms and opposites ji covering use of the word 'routine ' in such areas as economics, organization theory and z artificial intelligence. 6
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 realtime behavi ..."
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Cited by 44 (10 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...
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 44 (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.
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 43 (8 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...
Parallel Algorithms for Integer Factorisation
"... The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the RivestShamirAdelman (RSA) system, depends o ..."
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Cited by 41 (17 self)
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The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the RivestShamirAdelman (RSA) system, depends on the difficulty of factoring the public keys. In recent years the best known integer factorisation algorithms have improved greatly, to the point where it is now easy to factor a 60decimal digit number, and possible to factor numbers larger than 120 decimal digits, given the availability of enough computing power. We describe several algorithms, including the elliptic curve method (ECM), and the multiplepolynomial quadratic sieve (MPQS) algorithm, and discuss their parallel implementation. It turns out that some of the algorithms are very well suited to parallel implementation. Doubling the degree of parallelism (i.e. the amount of hardware devoted to the problem) roughly increases the size of a number which can be factored in a fixed time by 3 decimal digits. Some recent computational results are mentioned – for example, the complete factorisation of the 617decimal digit Fermat number F11 = 2211 + 1 which was accomplished using ECM.