pinecone/core-2020-05-10-deduplication huggingface dataset:
Multiple Product Modulo Arbitrary Numbers

AbstractLetnbinary numbers of lengthnbe given. The Boolean function “Multiple Product”MPnasks for (some binary representation of ) the value of their product. It has been shown (K.-Y. Siu and V. Roychowdhury, On optimal depth threshold circuits for multiplication and related problems,SIAM J. Discrete Math.7, 285–292 (1994)) that this function can be computed in polynomial-size threshold circuits of depth 4. For many other arithmetic functions, circuits of depth 3 are known. They are mostly based on the fact that the value of the considered function modulo some prime numbers p can be computed easily in threshold circuits of depth 2. In this paper, we investigate the complexity of computingMPnmodulomby depth-2 threshold circuits. It turns out that for all but a few integersm, exponential size is required. In particular, it is shown that form∈{2, 4, 8}, polynomial-size circuits exist, form∈{3, 6, 12, 24}, the question remains open and in all other cases, exponential-size circuits are required. The result still holds if we allowmto grow withn
On the Power of DNA-Computing

AbstractAdleman used biological manipulations with DNA strings to solve some instances of the Directed Hamiltonian Path Problem. Lipton showed how to extend this idea to solve any NP problem. We prove that exactly the problems in PNP=Δp2can be solved in polynomial time using Lipton's model. Various modifications of Lipton's model, based on other DNA manipulations, are investigated systematically, and it is proved that their computational power in polynomial time can be characterized by one of the complexity classes P,Δp2, orΔp3
Randomness in Distribution Protocols

AbstractRandomness is a useful computation resource due to its ability to enhance the capabilities of other resources. Its interaction with resources such as time, space, interaction with provers and its role in several areas of computer science has been extensively studied. In this paper we give a systematic analysis of the amount of randomness needed by secret sharing schemes and secure key distribution schemes. We give both upper and lower bounds on the number of random bits needed by secret sharing schemes. The bounds are tight for several classes of secret sharing schemes. For secure key distribution schemes we provide a lower bound on the amount of randomness needed, thus showing the optimality of a recently proposed key distribution protocol
Bisimulation for Higher-Order Process Calculi

AbstractAhigher-order process calculusis a calculus for communicating systems which contains higher-order constructs like communication of terms. We analyse the notion ofbisimulationin these calculi. We argue that both the standard definition of bisimulation (i.e., the one for CCS and related calculi), as well ashigher-order bisimulation[E. Astesiano, A. Giovini, and G. Reggio,in“STACS '88,” Lecture Notes in Computer Science, Vol. 294, pp. 207–226, Springer-Verlag, Berlin/New York, 1988; G. Boudol,in“TAPSOFT '89,” Lecture Notes in Computer Science, Vol. 351, pp. 149–161, Springer-Verlag, Berlin/New York, 1989; B. Thomsen, Ph.D. thesis, Dept. of Computing, Imperial College, 1990] are in general unsatisfactory, because of their over-discrimination. We propose and study a new form of bisimulation for such calculi, calledcontext bisimulation, which yields a more satisfactory discriminanting power. A drawback of context bisimulation is the heavy use of universal quantification in its definition, which is hard to handle in practice. To resolve this difficulty we introducetriggered bisimulationandnormal bisimulation, and we prove that they both coincide with context bisimulation. In the proof, we exploit thefactorisation theorem: When comparing the behaviour of two processes, it allows us to “isolate” subcomponents which might give differences, so that the analysis can be concentrated on the
Region-Based Memory Management

AbstractThis paper describes a memory management discipline for programs that perform dynamic memory allocation and de-allocation. At runtime, all values are put intoregions. The store consists of a stack of regions. All points of region allocation and de-allocation are inferred automatically, using a type and effect based program analysis. The scheme does not assume the presence of a garbage collector. The scheme was first presented in 1994 (M. Tofte and J.-P. Talpin,in“Proceedings of the 21st ACM SIGPLAN–SIGACT Symposium on Principles of Programming Languages,” pp. 188–201); subsequently, it has been tested in The ML Kit with Regions, a region-based, garbage-collection free implementation of the Standard ML Core language, which includes recursive datatypes, higher-order functions and updatable references L. Birkedal, M. Tofte, and M. Vejlstrup, (1996),in“Proceedings of the 23 rd ACM SIGPLAN–SIGACT Symposium on Principles of Programming Languages,” pp. 171–183. This paper defines a region-based dynamic semantics for a skeletal programming language extracted from Standard ML. We present the inference system which specifies where regions can be allocated and de-allocated and a detailed proof that the system is sound with respect to a standard semantics. We conclude by giving some advice on how to write programs that run well on a stack of regions, based on practical experience with the ML Kit
Approximation Algorithms for Time Constrained Scheduling

AbstractIn this paper we consider the following time constrained scheduling problem. Given a set of jobsJwith execution timese(j)∈(0, 1] and an undirected graphG=(J, E), we consider the problem to find a schedule for the jobs such that adjacent jobs (j, j′)∈Eare assigned to different machines and that the total execution time for each machine is at most 1. The goal is to find a minimum number of machines to execute all jobs under this time constraint. This scheduling problem is a natural generalization of the classical bin-packing problem. We propose and analyse several approximation algorithms with constant absolute worst case ratio for graphs that can be colored in polynomial time
Normalization Results for Typeable Rewrite Systems

AbstractIn this paper we introduce Curryfied term rewriting systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts andω. Three operations on types—substitution, expansion, and lifting—are used to define type assignment and are proved to be sound. With this result the system is proved closed for reduction. Using a more liberal approach to recursion, we define a general scheme for recursive definitions and prove that, for all systems that satisfy this scheme, every term typeable without using the type-constantωis strongly normalizable. We also show that, under certain restrictions, all typeable terms have a (weak) head-normal form, and that terms whose type does not containωare normalizable
Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes

AbstractThe communication power of the one-way and two-way edge-disjoint path modes for broadcast and gossip is investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). The main results achieved are the following: 1. For each connected graphGnofnnodes, the complexity of broadcast inGn,Bmin(Gn), satisfies ⌈log2n⌉⩽Bmin(Gn)⩽⌈log2n⌉+1. The complete binary trees meet the upper bound, and all graphs containing a Hamiltonian path meet the lower bound. 2. For each connected graphGnofnnodes, the one-way (two-way) gossip complexityR(Gn) (R2(Gn)) satisfies⌈log2n⌉⩽R2(Gn)⩽2·⌈log2n⌉+1,1.44...log2n⩽R(Gn)⩽2·⌈log2n⌉+2.All these lower and upper bounds are shown to be sharp up to 1. 3. All planar graphs ofnnodes and degreehhave a two-way gossip complexity of at least 1.5log2n−log2log2n−0.5log2h−8, and the two-dimensional grid ofnnodes has the gossip complexity 1.5log2n−log2log2n±O(1); i.e., two-dimensional grids are optimal gossip structures among planar graphs of bounded degree. Some upper bounds are also obtained for the one-way mode. 4. Thed-dimensional grid,d⩾3, ofnnodes has the two-way gossip complexity (1+1/d)·log2n−log2nlog2n±O(d)
Strong Normalization from Weak Normalization in Typedλ-Calculi

AbstractFor some typedλ-calculi it is easier to prove weak normalization than strong normalization. Techniques to infer the latter from the former have been invented over the last twenty years by Nederpelt, Klop, Khasidashvili, Karr, de Groote, and Kfoury and Wells. However, these techniques infer strong normalization of one notion of reduction from weak normalization of amore complicatednotion of reduction. This paper presents a new technique to infer strong normalization of a notion of reduction in a typedλ-calculus from weak normalization of thesamenotion of reduction. The technique is demonstrated to work on some well-known systems including second-orderλ-calculus and the system of positive, recursive types. It gives hope for a positive answer to the Barendregt–Geuvers conjecture stating that every pure type system which is weakly normalizing is also strongly normalizing. The paper also analyzes the relationship between the techniques mentioned above, and reviews, in less detail, other techniques for proving strong normalization
Determinization and Memoryless Winning Strategies

AbstractWe show that Safra's determinization ofω-automata with Streett (strong fairness) acceptance condition also gives memoryless winning strategies in infinite games, for the player whose acceptance condition is the complement of the Streett condition. Both determinization and memorylessness are essential parts of known proofs of Rabin's tree automata complementation lemma. Also, from Safra's determinization construction, along with its memoryless winning strategy extension, a single exponential complementation of Streett tree automata follows. A different single exponential construction and proof first appeared in [N. Klarlund (1992), Progress measures, immediate determinacy, and a subset construction for tree automata,in“Proceedings, 7th IEEE Symposium on Logics in Computer Science”]
Propositional Lax Logic

AbstractWe investigate a peculiar intuitionistic modal logic, called Propositional Lax Logic (PLL), which has promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness up to behavioural constraints—a central notion in hardware verification—as a logical modality. As a modal logic it is special since it features a single modal operator ○ that has a flavour both of possibility and of necessity. In the paper we provide the motivation for PLL and present several technical results. We investigate some of its proof-theoretic properties, presenting a cut-elimination theorem for a standard Gentzen-style sequent presentation of the logic. We go on to define a new class of fallible two-frame Kripke models for PLL. These models are unusual since they feature worlds with inconsistent information; furthermore, the only frame condition imposed is that the ○-frame be a subrelation of the ⊃-frame. We give a natural translation of these models into Goldblatt's J-space models of PLL. Our completeness theorem for these models yields a Gödel-style embedding of PLL into a classical bimodal theory of type (S4,S4) and underpins a simple proof of the finite model property. We proceed to prove soundness and completeness of several theories for specialized classes of models. We conclude with a brief exploration of two concrete and rather natural types of model from hardware verification for which the modality ○ models correctness up to timing constraints. We obtain decidability of ○-free fragment of the logic of the first type of model, which coincides with the stable form of Maksimova's intermediate logicLΠ
The Bounded Degree Problem for eNCE Graph Grammars

AbstractThe complexity of the bounded degree problem is analyzed for graph languages generated by eNCE graph grammars. In particular, the bounded degree problem is shown to be undecidable for eNCE graph grammars, DEXPTIME-complete for confluent/boundary eNCE graph grammars, PSPACE-complete for linear eNCE graph grammars, and P-complete for non-blocking eNCE graph grammars. In our main theorem we show that the bounded degree problem is NL-complete for reduced non-blocking eNCE graph grammars. Many of the shown results carry over to other types of graph grammars
Models of Multi-user Write-Efficient Memories and General Diametric Theorems

AbstractWrite-efficient memories (WEM) were introduced by Ahlswede/Zhang as a model for storing and updating information on a rewritable medium. We strengthen the capacity theorem by providing a full control of the rates of the spreads. Next we address and settle the storage capacity region problem under the average costs constraint for the case of many users who write on the memory in an arbitrary order, where neither the encoder nor the decoder knows the previous content of the memory. The combinatorial essence is a diametric theorem for several families. Finally we present a storage capacity theorem for several persons using the memory in cyclic order
Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation

AbstractDisjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfounded-free models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the well-founded WPoperator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function-free programs. The algorithm's soundness and completeness are proved and some complexity issues are discussed
Improved Parallel Integer Sorting without Concurrent Writing

AbstractWe show thatnintegers in the range 1,…,ncan be sorted stably on an EREW PRAM usingO(t) time andO(n(lognloglogn+(logn)2/t)) operations, for arbitrary givent⩾lognloglogn, and on a CREW PRAM usingO(t) time andO(n(logn+logn/2t/logn)) operations, for arbitrary givent⩾logn. In addition, we are able to sortnarbitrary integers on a randomized CREW PRAM within the same resource bounds with high probability. In each case our algorithm is a factor of almostΘ:(logn) closer to optimality than all previous algorithms for the stated problem in the stated model, and our third result matches the operation count of the best previous sequential algorithm. We also show thatnintegers in the range 1,…,mcan be sorted inO((logn)2) time withO(n) operations on an EREW PRAM using a nonstandard word length ofO(lognloglognlogm) bits, thereby greatly improving the upper bound on the word length necessary to sort integers with a linear time–processor product, even sequentially. Our algorithms were inspired by, and in one case directly use, the fusion trees of Fredman and Willard
Triangulating Planar Graphs While Minimizing the Maximum Degree

AbstractIn this paper we consider the problem how to augment a planar graph to a triangulated planar graph while minimizing the maximum degree increase. We show that the general problem is NP-complete for bi-connected planar graphs. An approximation algorithm is presented to triangulate triconnected planar graphs such that the maximum degree of the triangulation is at mostd+8, wheredis the maximum degree of the input graph. Generalizing this result yields a triangulation algorithm for general planar graphs with maximum degree at most an additional constant larger than existing lower bounds
The Kolmogorov Expression Complexity of Logics

AbstractThe purpose of the paper is to propose a completely new notion of complexity of logics in finite-model theory. It is the Kolmogorov variant of the Vardi'sexpression complexity. We define it by considering the value of the Kolmogorov complexityC(L[A]) of the infinite stringL[A] of all truth values of sentences ofLin A. The higher is this value, the more expressive is the logicLin A. If D is a class of finite models, then the value ofC(L[A]) over all A∈D is a measure of expressive power ofLin D. Unboundedness ofC(L[A])−C(L′[A]) for A∈D implies nonexistence of a recursive interpretation ofLinL′. A version of this statement with complexities modulo oracles implies the nonexistence of any interpretation ofLinL′. Thus the valuesC(L[A]) modulo oracles constitute an invariant of the expressive power of logics over finite models, depending on their real (absolute) expressive power, and not on the syntax. We investigate our notion for fragments of the infinitary logic Lω∞ω: least fixed point logic (LFP) and partial fixed point logic (PFP). We prove a precise characterization of 0–1 laws for these logics in terms of a certain boundedness condition placed onC(L[A]). We get an extension of the notion of a 0–1 law by imposing an upper bound on the value ofC(L[A]) growing not too fast with cardinality of A, which still implies inexpressibility results similar to those implied by 0–1 laws. We also discuss classes D in whichC(PFPk[A]) is very high. It appears that then PFP or its simple extension can define all the PSPACE subsets of D
Constraint Logic Programming with Dynamic Scheduling: A Semantics Based on Closure Operators

AbstractThe first logic programming languages, such as Prolog, used a fixed left-to-right atom scheduling rule. Recent logic programming languages, however, provide more flexible scheduling in which there is a default computation rule such as left-to-right but in which some calls are dynamically “delayed” until their arguments are sufficiently instantiated to allow the call to run efficiently. Such languages include constraint logic programming languages, since most implementations of these languages delay constraints which are “too hard.” From the semantic point of view, the fact that an atom must be delayed under certain conditions, causes the standard semantics of (constraint) logic programming to be no longer adequate to capture the meaning of a program. In our paper we attack this problem and we develop a denotational semantics for constraint logic programming with dynamic scheduling. The key idea is that the denotation of an atom or goal is a set of closure operators, where different closure operators correspond to different sequences of rule choices
Measure on P: Strength of the Notion

AbstractWe give a notion of measure at P in a paradigm that differs somewhat from the standard theory. Our new notion overcomes some limitations of earlier formulations, specifically, concerning closure of null sets under union. First, we analyze formally some of the difficulties in defining measure at P. We then present the new definitions and determine the basic properties of the notion, including the density and immunity characteristics of a random language. We argue that these results are parallel to previous measure results at exponential time
Simulating Shared Memory in Real Time: On the Computation Power of Reconfigurable Architectures

AbstractWe consider randomized simulations of shared memory on a distributed memory machine (DMM) where thenprocessors and thenmemory modules of the DMM are connected via a reconfigurable architecture. We first present a randomized simulation of a CRCW PRAM on a reconfigurable DMM having a complete reconfigurable interconnection. It guarantees delay O(log*n), with high probability. Next we study a reconfigurable mesh DMM (RM-DMM). Here thenprocessors andnmodules are connected via ann×nreconfigurable mesh. It was already known that ann×mreconfigurable mesh can simulate in constant time ann-processor CRCW PRAM with shared memory of sizem. In this paper we present a randomized step by step simulation of a CRCW PRAM with arbitrarily large shared memory on an RM-DMM. It guarantees constant delay with high probability, i.e., it simulates in real time. Finally we prove a lower bound showing that sizeΩ(n2) for the reconfigurable mesh is necessary for real time simulations
An Equational Axiomatization for Multi-exit Iteration

AbstractThis paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutions of systems of recursion equations of the formX1=defP1X2+Q1⋮Xn=defPnX1+Qn,wherenis a positive integer and thePiand theQiare process terms. The addition of multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA*). As a consequence, the proof of completeness of the proposed equational axiomatization for this language, although standard in its general structure, is much more involved than that for BPA*. An expressiveness hierarchy for the family ofk-exit iteration operators proposed by Bergstra, Bethke, and Ponse is also offered
Efficient Learning of Typical Finite Automata from Random Walks

AbstractThis paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the “typical” labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning non-trivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that makes an expected polynomial number of mistakes in this model. Next, we show how this first algorithm can be used as a subroutine by a second algorithm that also makes a polynomial number of mistakes even in the absence of a reset. Along the way, we prove a number of combinatorial results for randomly labeled automata. We also show that the labeling of the states and the bits of the input sequence need not be truly random, but merelysemi-random. Finally, we discuss an extension of our results to a model in which automata are used to represent distributions over binary strings
Lambda Calculus with Explicit Recursion

AbstractThis paper is concerned with the study ofλ-calculus with explicit recursion, namely of cyclicλ-graphs. The starting point is to treat aλ-graph as a system of recursion equations involvingλ-terms and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the substitution operation. This leads to a family ofλ-graph calculi, which can be seen as an extension of the family ofλσ-calculi (λ-calculi with explicit substitution). While theλσ-calculi treat the let-construct as a first-class citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of program