pinecone/core-2020-05-10-deduplication huggingface dataset:
Sparse Sets and Collapse of Complexity Classes

AbstractIn this paper a new upward separation technique is developed. It is applied to prove that for a class of functions F a separation DTIME(F)≠NTIME(F) can be characterized by the existence of (not only polynomially) sparse sets in certain complexity classes. As a consequence, a solution of an open question of J. Hartmanis (1983, Inform. Process. Lett.16, 55–60) is obtained: There is an nO(log n)–sparse set in NP−P iff ∪c>1NTIME(2c□n)≠∪c>1DTIME(2c□n). Further we prove that there is an nO(log n)–sparse set in NP−coNP iff ∪c>1NTIME(2c□n)≠∪c>1coNTIME(2c□n). The technique also allows us to characterize the existence of sets of different densities in NP−P by the existence of slightly denser sets in NTIME(F)−DTIME(F) for certain classes of functions F. For example, there is an nO(log n)–sparse set in NP−P iff there is an nO((log n)3)–sparse set in ∪c>1NTIME(nclog n)−∪c>1DTIME(nclog n). The end of the paper is devoted to limitations of the technique
Delayed Information and Action in On-Line Algorithms

AbstractMost on-line analysis assumes that, at each time step, all relevant information up to that time step is available and a decision has an immediate effect. In many on-line problems, however, the time when relevant information is available and the time a decision has an effect may be decoupled. For example, when making an investment, one might not have completely up-to-date information on market prices. Similarly, a buy or sell order might only be executed some time in the future. We introduce and explore natural delayed models for several well-known on-line problems. Our analyses demonstrate the importance of considering timeliness in determining the competitive ratio of an on-line algorithm. For many problems, we demonstrate that there exist algorithms with small competitive ratios even when large delays affect the timeliness of information and the effect of decisions
Learning Fixed-Dimension Linear Thresholds from Fragmented Data

AbstractWe investigate PAC-learning in a situation in which examples (consisting of an input vector and 0/1 label) have some of the components of the input vector concealed from the learner. This is a special case of restricted focus of attention (RFA) learning. Our interest here is in 1-RFA learning, where only a single component of an input vector is given, for each example. We argue that 1-RFA learning merits special consideration within the wider field of RFA learning. It is the most restrictive form of RFA learning (so that positive results apply in general), and it models a type of “data fusion” scenario, where we have sets of observations from a number of separate sensors, but these sensors are uncorrelated sources. Within this setting we study the well-known class of linear threshold functions, the characteristic functions of Euclidean half-spaces. The sample complexity (i.e., sample-size requirement as a function of the parameters) of this learning problem is affected by the input distribution. We show that the sample complexity is always finite, for any given input distribution, but we also exhibit methods for defining “bad” input distributions for which the sample complexity can grow arbitrarily fast. We identify fairly general sufficient conditions for an input distribution to give rise to sample complexity that is polynomial in the PAC parameters ϵ−1 and δ−1. We give an algorithm whose sample complexity is polynomial in these parameters and the dimension (number of input components), for input distributions that satisfy our conditions. The run-time is polynomial in ϵ−1 and δ−1 provided that the dimension is any constant. We show how to adapt the algorithm to handle uniform misclassification noise
Contextual Petri Nets, Asymmetric Event Structures, and Processes

AbstractWe present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (read-only operations). A basic role is played by asymmetric event structures, a generalization of Winskel's prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel's seminal work on safe nets, the truly concurrent event-based semantics of contextual nets is given at categorical level via a chain of coreflections leading from the category SW-CN of semi-weighted contextual nets to the category Dom of finitary prime algebraic domains. First an unfolding construction generates from a contextual net a corresponding occurrence contextual net, from where an asymmetric event structure is extracted. Then the configurations of the asymmetric event structure, endowed with a suitable order, are shown to form a finitary prime algebraic domain. We also investigate the relation between the proposed unfolding semantics and several deterministic process semantics for contextual nets in the literature. In particular, the domain obtained via the unfolding is characterized as the collection of the deterministic processes of the net endowed with a kind of prefix ordering
The Query Complexity of Finding Local Minima in the Lattice

AbstractIn this paper we study the query complexity of finding local minimum points of a boolean function. This task occurs frequently in exact learning algorithms for many natural classes, such as monotone DNF, O(log n)-term DNF, unate DNF, and decision trees. On the negative side, we prove that any (possibly randomized) algorithm that produces a local minimum of a function f chosen from a sufficiently “rich” concept class, using a membership oracle for f, must ask Ω(n2) membership queries in the worst case. In particular, this lower bound applies to the class of decision trees. A simple algorithm is known that achieves this lower bound. On the positive side, we show that for the class O(log n)-term DNF finding local minimum points requires only Θ(n log n) membership queries (and more generally Θ(tn) membership queries for t-term DNF with t≤n). This efficient procedure improves the time and query complexity of known learning algorithms for the class O(log n)-term DNF
Suboptimal Measures of Predictive Complexity for Absolute Loss Function

AbstractThe problem of existence of predictive complexity for the absolute loss game is studied. Predictive complexity is a generalization of Kolmogorov complexity which bounds the ability of any algorithm to predict elements of a sequence of outcomes. For perfectly mixable loss functions (logarithmic and squared difference are among them) predictive complexity is defined like Kolmogorov complexity to within an additive constant. The absolute loss function is not perfectly mixable, and the question of existence of the corresponding predictive complexity, which is defined to within an additive constant, is open. We prove that in the case of the absolute loss game the predictive complexity can be defined to within an additive term O(n), where n is the length of a sequence of outcomes. We prove also that in some restricted settings this bound cannot be improved
Abstract State Machines and Computationally Complete Query Languages

AbstractAbstract state machines (ASMs) form a relatively new computation model holding the promise that they can simulate any computational system in lockstep. In particular, an instance of the ASM model has recently been introduced for computing queries to relational databases. This model, to which we refer as the BGS model, provides a powerful query language in which all computable queries can be expressed. In this paper, we show that when one is only interested in polynomial- time computations, BGS is strictly more powerful than both QL and whilenew, two well-known computationally complete query languages. We then show that when a language such as whilenew is extended with a duplicate elimination mechanism, polynomial-time simulations between the language and BGS become possible
Communication Complexity Method for Measuring Nondeterminism in Finite Automata

AbstractWhile deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata. In this paper the concept of communication complexity is applied in order to achieve progress in this problem area. The main results are as follows:1. Deterministic communication complexity provides lower bounds on the size of nfa's with bounded unambiguity. Applying this fact, the proofs of several results about nfa's with limited ambiguity can be simplified and presented in a uniform way.2. There is a family of languages KONk2 with an exponential size gap between nfa's with polynomial leaf number/ambiguity and nfa's with ambiguity k. This partially provides an answer to the open problem posed by B. Ravikumar and O. Ibarra (1989, SIAM J. Comput.18, 1263–1282) and H. Leung (1998, SIAM J. Comput.27, 1073–1082)
Clausal Logic and Logic Programming in Algebraic Domains

AbstractWe introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo
Decidability of Split Equivalence

AbstractWe show that the following problem is decidable: given expressions E1 and E2 constructed from variables by the regular operations and shuffle, is the identity E1=E2 true for all instantiations of its variables by strings? Our proof uses the notations developed in the causal approach to concurrency. As a byproduct we obtain decidability of similar equivalence for other formalisms. In particular, we prove decidability of split equivalence for Petri nets. Our paper also provides an alternative proof for a characterization of split equivalence recently given by W. Vogler
The Nonapproximability of OBDD Minimization

AbstractThe size of ordered binary decision diagrams (OBDDs) is determined by the chosen variable ordering. A poor choice may cause an OBDD to be too large to fit into the available memory. The decision variant of the variable ordering problem is known to be NP-complete. We strengthen this result by showing that, unless P=NP, for each constant c>1 there is no polynomial time approximation algorithm with the performance ratio c for the variable ordering problem, i.e., no polynomial time algorithm that guarantees the computation of a variable ordering so that the resulting OBDD size is larger than the minimum size by a factor of at most c. This result justifies, also from a theoretical point of view, the use of heuristics for the variable ordering problem
Rationality in Algebras with a Series Operation

AbstractWe consider the notion of rationality in algebras with a designated binary associative operation called the series operation, or the sequential product. We define automata operating in these algebras and rational expressions matching their expressive power, and we show that this expressive power equals that of algebraic recognizability. The framework which we consider encompasses both the free semigroup and the term algebras and the restriction of our results to these special cases coincides exactly with the classical results on recognizability (Kleene, Myhill, and Nerode for word languages, and Thatcher and Wright for term languages). Next we consider the behavior of the automata and the rational expression which we introduce when conditions such as associativity and commutativity are imposed on the term operations. We also characterize algebraically, syntactically and automata-theoretically the languages which have a bound on the number of nested occurrences of certain designated term operations. Finally, we consider the applications of our results to the languages of series-parallel labelled posets
Trace and Testing Equivalence on Asynchronous Processes

AbstractWe study trace and may-testing equivalences in the asynchronous versions of CCS and π-calculus. We start from the operational definition of the may-testing preorder and provide finitary and fully abstract trace-based characterizations for it, along with a complete in-equational proof system. We also touch upon two variants of this theory by first considering a more demanding equivalence notion (must-testing) and then a richer version of asynchronous CCS. The results throw light on the difference between synchronous and asynchronous communication and on the weaker testing power of asynchronous observations
Nonerasing, Counting, and Majority over the Linear Time Hierarchy

AbstractIn this paper, we investigate several extensions of the linear time hierarchy (denoted by LTH). We first prove that it is not necessary to erase the oracle tape between two successive oracle calls, thereby lifting a common restriction on LTH machines. We also define a natural counting extension of LTH and show that it corresponds to a robust notion of counting bounded arithmetic predicates. Finally, we show that the computational power of the majority operator is equivalent to that of the exact counting operator in both contexts
Online Variable Sized Covering

AbstractWe consider one-dimensional and multidimensional vector covering with variable sized bins. In the one-dimensional case, we consider variable sized bin covering with bounded item sizes. For every finite set of bins B, and upper bound 1/m on the size of items for some integer m, we define a ratio r(B, m). We prove this is the best possible competitive ratio for the set of bins B and the parameter m by giving both an algorithm with competitive ratio r(B, m) and an upper bound of r(B, m) on the competitive ratio of any online deterministic or randomized algorithm. The ratio satisfies r(B, m)≥m/(m+1) and equals this number if all bins are of size 1. For multidimensional vector covering we consider the case where each bin is a binary d-dimensional vector. It was shown by N. Alon, Y. Azar, J. Csirik, L. Epstein, S. V. Sevastianov, A. P. A. Vestjens, and G. J. Woeginger (1998, Algorithmica 21, 104–118) that if B contains a single bin which is all 1, then the best competitive ratio is Θ(1/d). We show an upper bound of 1/2d(1−o(1)) for the general problem, and consider four special case variants. We show an algorithm with optimal competitive ratio 1/2 for the model where each bin in B is a standard basis vector. We consider the model where B consists of all unit prefix vectors. A unit prefix vector has i leftmost components of 1, and all other components are 0. We show that this model is harder than the case of standard basis vector bins by giving an upper bound of O(1/log d) on the competitive ratio of any deterministic or randomized algorithm. Next, we discuss the model where B contains all binary vectors. We show this model is easier than the model of one bin type which is all 1 by giving an algorithm with competitive ratio Ω(1/log d). The most interesting multidimensional case is d=2. The results of N. Alon et al. give a 0.25-competitive algorithm for B={(1, 1)} and an upper bound of 0.4 on the competitive ratio of any algorithm. In this paper we consider all other models for d=2. For standard basis vectors, we give an algorithm with optimal competitive ratio 1/2. For unit prefix vectors we give an upper bound of 4/9 on the competitive ratio of any deterministic or randomized algorithm. For the model where B consists of all binary vectors, we design an algorithm with ratio larger than 0.4. These results show that all above relations between models hold for d=2 as well
Distributed Probabilistic Polling and Applications to Proportionate Agreement

AbstractThis paper considers a probabilistic local polling process, examines its properties, and proposes its use in the context of distributed network protocols for achieving consensus. The resulting consensus algorithm is very simple and lightweight, yet it enjoys some desirable properties, such as proportionate agreement (namely, reaching a consensus value of one with probability proportional to the number of ones in the inputs), resilience against dynamic link failures and recoveries, and (weak) self-stabilization. The paper also investigates the maximum influence of small sets and establishes results analogous to those obtained for the problem in the deterministic polling model
Resource Access Control in Systems of Mobile Agents

AbstractWe describe a typing system for a distributed π-calculus which guarantees that distributed agents cannot access the resources of a system without first being granted the capability to do so. The language studied allows agents to move between distributed locations and to augment their set of capabilities via communication with other agents. The type system is based on the novel notion of a location type, which describes the set of resources available to an agent at a location. Resources are themselves equipped with capabilities, and thus an agent may be given permission to send data along a channel at a particular location without being granted permission to read data along the same channel. We also describe a tagged version of the language, where the capabilities of agents are made explicit in the syntax. Using this tagged language we define access violations as runtime errors and prove that well-typed systems are incapable of such errors
Efficient and Flexible Matching of Recursive Types

AbstractEquality and subtyping of recursive types were studied in the 1990s by Amadio and Cardelli; Kozen, Palsberg, and Schwartzbach; Brandt and Henglein; and others. Potential applications include automatic generation of bridge code for multilanguage systems and type-based retrieval of software modules from libraries. In this paper, we present an efficient decision procedure for a notion of type equality that includes unfolding of recursive types, and associativity and commutativity of product types. Advocated by Auerbach, Barton, and Raghavachari, these properties enable flexible matching of types. For two types of size at most n, our algorithm takes O(n) iterations each of which takes O(n) time, for a total of O(n2) time
The Complexity of Propositional Linear Temporal Logics in Simple Cases

AbstractIt is well known that model checking and satisfiability for PLTL are PSPACE-complete. By contrast, very little is known about whether there exist some interesting fragments of PLTL with a lower worst-case complexity. Such results would help understand why PLTL model checkers are successfully used in practice. In this article we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height
Reduction of Permutation-Invariant Polynomials A Noncommutative Case Study

AbstractLet R be a commutative ring with 1, let R〈X1,…,Xn〉/I be the polynomial algebra in the n≥4 noncommuting variables X1,…,Xn over R modulo the set of commutator relations I={(X1+···+Xn)∗Xi=Xi∗(X1+···+Xn)|1≤i≤n}. Furthermore, let G be an arbitrary group of permutations operating on the indeterminates X1,…,Xn, and let R〈X1,…,Xn〉/IG be the R-algebra of G-invariant polynomials in R〈X1,…,Xn〉/I. The first part of this paper is about an algorithm, which computes a representation for any f∈R〈X1,…,Xn〉/IG as a polynomial in multilinear G-invariant polynomials, i.e., the maximal variable degree of the generators of R〈X1,…,Xn〉/IG is at most 1. The algorithm works for any ring R and for any permutation group G. In addition, we present a bound for the number of necessary generators for the representation of all G-invariant polynomials in R〈X1,…,Xn〉/IG with a total degree of at most d. The second part contains a first but promising analysis of G-invariant polynomials of solvable polynomial rings
Formative Processes with Applications to the Decision Problem in Set Theory I. Powerset and Singleton Operators

AbstractThis paper introduces formative processes, composed by transitive partitions. Given a family F of sets, a formative process ending in the Venn partition Σ of F is shown to exist. Sufficient criteria are also singled out for a transitive partition to model (via a function from set variables to unions of sets in the partition) all set-literals modeled by Σ. On the basis of such criteria a procedure is designed that mimics a given formative process by another where sets have finite rank bounded by C(|Σ|), with C a specific computable function. As a by-product, one of the core results on decidability in computable set theory is rediscovered, namely the one that regards the satisfiability of unquantified set-theoretic formulae involving Boolean operators, the singleton-former, and the powerset operator. The method described (which is able to exhibit a set-solution when the answer is affirmative) can be extended to solve the satisfiability problem for broader fragments of set theory
Aliasing Models for Mobile Objects

AbstractIn Obliq, a lexically scoped, distributed, object-oriented programming language, object migration was suggested as the creation of a copy of the state of an object at the target site, followed by turning the object itself into an alias, also called surrogate, for the remote copy. We consider the creation of object surrogates as an abstraction of the above-mentioned style of migration. We introduce Øjeblik, a typed distribution-free subset of Obliq, and provide four different configuration-style semantics, which only differ in the respective aliasing model. We show that two of the semantics, one of which matches Obliq's implementation, render migration unsafe, while our new proposal allows for safe migration at least for a large class of program contexts. In addition, we propose a type system that allows a programmer to statically guarantee that programs belong to that class. Our work suggests a straightforward repair of Obliq's aliasing model
Syntactic Type Soundness Results for the Region Calculus

AbstractThe region calculus of Tofte and Talpin is a polymorphically typed lambda calculus with annotations that make memory allocation and deallocation explicit. It is intended as an intermediate language for implementing Hindley-Milner typed functional languages such as ML without traditional trace-based garbage collection. Static region and effect inference can be used to annotate a statically typed ML program with memory management primitives. Soundness of the calculus with respect to the region and effect system is crucial to guarantee safe deallocation of regions, i.e., deallocation should only take place for objects which are provably dead. The original soundness proof by Tofte and Talpin requires a complex co-inductive safety relation. In this paper, we present two small-step operational semantics for the region calculus and prove their type soundness with respect to the region and effect system. Following the standard syntactic approach of Wright, Felleisen, and Harper, we obtain simple inductive proofs. The first semantics is store-less. It is simple and elegant and gives rise to perspicuous proofs. The second semantics provides a store-based model for the region calculus. Albeit slightly more complicated, its additional expressiveness allows us to model operations on references with destructive update. A pure fragment of both small-step semantics is then proven equivalent to the original big-step operational approach of Tofte and Talpin. This leads to an alternative soundness proof for their evaluation-style formulation