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The Impact of the Lambda Calculus in Logic and Computer Science
 Bulletin of Symbolic Logic
, 1997
"... One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the represent ..."
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One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand. Acknowledgement. The following persons provided help in various ways. Erik Barendsen, Jon Barwise, Johan van Benthem, Andreas Blass, Olivier Danvy, Wil Dekkers, Marko van Eekelen, Sol Feferman, Andrzej Filinski, Twan Laan, Jan Kuper, Pierre Lescanne, Hans Mooij, Robert Maron, Rinus Plasmeijer, Randy Pollack, Kristoffer Rose, Richard Shore, Rick Statman and Simon Thompson. Partial support came from the European HCM project Typed lambda calculus (CHRXCT920046), the Esprit Working Group Types (21900) and the Dutch NWO project WINST (612316607). 1. Introduction This paper is written to honor Church's gr...
Proving primality in essentially quartic random time
 Math. Comp
, 2003
"... Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1. ..."
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Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1.
OffLine and OnLine CallScheduling in Stars and Trees
 in Proceedings of the 23rd International Workshop on GraphTheoretic Concepts in Computer Science, WG ‘97, LNCS1335, SpringerVerlag
, 1997
"... . Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the callschedulin ..."
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. Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the callscheduling problem is studied for star and tree networks. Lower and upper bounds on the worstcase performance of ListScheduling (LS) and variants of it are obtained for callscheduling with arbitrary bandwidth requirements and either unit call durations or arbitrary call durations. LS does not require advance knowledge of call durations and, hence, is an online algorithm. It has performance ratio (competitive ratio) at most 5 in star networks. A variant of LS for calls with unit durations is shown to have performance ratio at most 2 2 3 . In tree networks with n nodes, a variant of LS for calls with unit durations has performance ratio at most 6, and a variant for calls with arbitrary d...
Complexity Theoretical Results for Randomized Branching Programs
, 1998
"... This work is settled in the area of complexity theory for restricted variants of branching programs. Today, branching programs can be considered one of the standard nonuniform models of computation. One reason for their popularity is that they allow to describe computations in an intuitively straigh ..."
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This work is settled in the area of complexity theory for restricted variants of branching programs. Today, branching programs can be considered one of the standard nonuniform models of computation. One reason for their popularity is that they allow to describe computations in an intuitively straightforward way and promise to be easier to analyze than the traditional models. In complexity theory, we are mainly interested in upper and lower bounds on the size of branching programs. Although proving superpolynomial lower bounds on the size of general branching programs still remains a challenging open problem, there has been considerable success in the study of lower bound techniques for various restricted variants, most notably perhaps readonce branching programs and OBDDs (ordered binary decision diagrams). Surprisingly, OBDDs have also turned out to be extremely useful in practical applications as a data structure for Boolean functions. So far, research has concentrated on determinis...
Approximation Algorithms for Survivable Optical Networks (Extended Abstract)
 In The 14th international Symposium on Distributed Computing (DISC
, 2000
"... ) T. Eilam S. Moran S. Zaks Department of Computer Science The Technion Haifa 32000, Israel email: feilam,moran,zaksg@cs.technion.ac.il We are motivated by the developments in alloptical networks  a new technology that supports high bandwidth demands. These networks provide a set of lightpa ..."
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) T. Eilam S. Moran S. Zaks Department of Computer Science The Technion Haifa 32000, Israel email: feilam,moran,zaksg@cs.technion.ac.il We are motivated by the developments in alloptical networks  a new technology that supports high bandwidth demands. These networks provide a set of lightpaths which can be seen as highbandwidth pipes on which communication is performed. Since the capacity enabled by this technology substantially exceeds the one provided by conventional networks, its ability to recover from failures within the optical layer is important. In this paper we study the design of a survivable optical layer. We assume that an initial set of lightpaths (designed according to the expected communication pattern) is given, and we are targeted at augmenting this initial set with additional lightpaths such that the result will guarantee survivability. For this purpose, we define and motivate a ring partition survivability condition that the solution must satisfy. Generally...
Factorizations of the ThompsonHigman groups, and circuit complexity”, Mathematics ArXiv: math.GR/0607349
, 2006
"... We consider the subgroup lpGk,1 of length preserving elements of the ThompsonHigman group Gk,1 and we show that all elements of Gk,1 have a unique lpGk,1 · Fk,1 factorization. This applies to the ThompsonHigman group Tk,1 as well. We show that lpGk,1 is a “diagonal ” direct limit of finite symmetr ..."
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We consider the subgroup lpGk,1 of length preserving elements of the ThompsonHigman group Gk,1 and we show that all elements of Gk,1 have a unique lpGk,1 · Fk,1 factorization. This applies to the ThompsonHigman group Tk,1 as well. We show that lpGk,1 is a “diagonal ” direct limit of finite symmetric groups, and that lpTk,1 is a k ∞ Prüfer group. We find an infinite generating set of lpGk,1 which is related to reversible boolean circuits. We further investigate connections between the ThompsonHigman groups, circuits, and complexity. We show that elements of Fk,1 cannot be oneway functions. We show that describing an element of Gk,1 by a generalized bijective circuit is equivalent to describing the element by a word over a certain infinite generating set of Gk,1; word length over these generators is equivalent to generalized bijective circuit size. We give some coNPcompleteness results for Gk,1 (e.g., the word problem when elements are given by circuits), and #Pcompleteness results (e.g., finding the lpGk,1 · Fk,1 factorization of an element of Gk,1 given by a circuit). 1
Aviv: A Retargetable Code Generator for Embedded Processors
, 1999
"... Embedded systems are broadly defined as systems designed for a particular application. The functionality of an embedded system is divided into hardware and software components. Synthesis of the hardware component involves designing a custom circuit for the hardware portion of the input application. ..."
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Embedded systems are broadly defined as systems designed for a particular application. The functionality of an embedded system is divided into hardware and software components. Synthesis of the hardware component involves designing a custom circuit for the hardware portion of the input application. Synthesis of the software component consists of designing a processor that is suited for the software portion of the input application and generating code that implements the functionality of the software component on the designed processor. Short design cycles and increasing embedded system complexity make it impractical to perform manual processor architecture exploration and code generation. In order to effectively explore the design space for the software component of embedded systems, a retargetable code generator is required. This thesis presents the Aviv retargetable code generator that generates optimized machine code for a specified target processor. Aviv is capable of compiling ap...
Programming by Logic and Logic by Programming (Extended Abstract)
 In Proceedings of SOFSEM'94 (Milovy, Czech Republic
, 1994
"... ) Paul J. Voda, J'an Komara Institute of Informatics, Comenius University Bratislava, Mlynsk'a dolina, 842 43 Bratislava, Slovakia. Email: voda@fmph.uniba.sk, komara@fmph.uniba.sk Abstract: This paper is an extended abstract of parts I and II of a monograph with the same title being prepared by ..."
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) Paul J. Voda, J'an Komara Institute of Informatics, Comenius University Bratislava, Mlynsk'a dolina, 842 43 Bratislava, Slovakia. Email: voda@fmph.uniba.sk, komara@fmph.uniba.sk Abstract: This paper is an extended abstract of parts I and II of a monograph with the same title being prepared by the authors. Logic was developed before the arrival of computers and it can be presented without reference to them. The main idea of the monograph is to stress the mutual links between logic and computer programming by taking those parts of logic which deal with computability and finitary logic (proof theory) and presenting them by employing the techniques of computer programming. The techniques involve the use of a good programming language with good data structures and proving the properties of functions written in this language. Keywords: computability, logic, computer programming 1 Introduction Nobody disputes the importance of mathematical logic to computer science but the influence...
Lower Bounds for (MOD p  MOD m) Circuits
 Proc. 39th IEEE FOCS
, 1998
"... Modular gates are known to be immune for the random restriction techniques of Ajtai (1983), Furst, Saxe, Sipser (1984), Yao (1985) and Hastad (1986). We demonstrate here a random clustering technique which overcomes this diculty and is capable to prove generalizations of several known modular circui ..."
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Modular gates are known to be immune for the random restriction techniques of Ajtai (1983), Furst, Saxe, Sipser (1984), Yao (1985) and Hastad (1986). We demonstrate here a random clustering technique which overcomes this diculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Therien (1990), Krause and Pudlak (1994), and others, characterizing symmetric functions computable by small (MOD p ; AND t ; MODm ) circuits. Applying a degreedecreasing technique together with random restriction methods for the AND gates at the bottom level, we also prove a hard special case of the Constant Degree Hypothesis of Barrington, Straubing, Therien (1990), and other related lower bounds for certain (MOD p ; MODm ; AND) circuits. Most of the previous lower bounds on circuits with modular gates used special denitions of the modular gates (i.e., the gate outputs one if the sum of its inputs is divisible by m, or is not divisible by m), and were not valid for more general MODm gates. Our methods are applicable, and our lower bounds are valid, for the most general modular gates as well. 1