Showing papers in "Information & Computation in 1984"
TL;DR: Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided and some relationships are shown to hold between the four concepts of merging.
Abstract: Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be confluent and terminating (modulo its permutative reductions). Further, some relationships are shown to hold between the four concepts of merging. © 1984 Academic Press, Inc.
1,064 citations
IBM1
TL;DR: A methodology of VLSI layout described by several authors first determines the relative positions of indivisible pieces, called cells, on the chip and orientation optimization for more general layouts is shown to be NP-complete (in the strong sense).
Abstract: A methodology of VLSI layout described by several authors first determines the relative positions of indivisible pieces, called cells, on the chip. Various optimizations are then performed on this initial layout to minimize some cost measure such as chip area or perimeter. If each cell is a rectangle with given dimensions, one optimization problem is to choose orientations of all the cells to minimize the cost measure. A polynomial time algorithm is given for this optimization problem for layouts of a special type called slicings. However, orientation optimization for more general layouts is shown to be NP-complete (in the strong sense).
326 citations
TL;DR: This paper disproves a conjecture made by Even and Yacobi (1980) that would imply nonexistence of public-key cryptosystems with NP-hard cracking problems and raises a new conjecture that implies that NP-complete sets cannot be accepted by Turing machines that have at most one accepting computation for each input word.
Abstract: A “promise problem” is a formulation of partial decision problem. Complexity issues about promise problems arise from considerations about cracking problems for public-key cryptosystems. Using a notion of Turing reducibility between promise problems, this paper disproves a conjecture made by Even and Yacobi (1980) , that would imply nonexistence of public-key cryptosystems with NP-hard cracking problems. In its place a new conjecture is raised having the same consequence. In addition, the new conjecture implies that NP-complete sets cannot be accepted by Turing machines that have at most one accepting computation for each input word.
309 citations
TL;DR: The article further develops Kolmogorov's algorithmic complexity theory, where the definition of randomness is modified to satisfy strong invariance properties (conservation inequalities) and concepts such as mutual information in individual infinite sequences are defined.
Abstract: The article further develops Kolmogorov's algorithmic complexity theory. The definition of randomness is modified to satisfy strong invariance properties (conservation inequalities). This allows definitions of concepts such as mutual information in individual infinite sequences. Applications to several areas, like probability theory, theory of algorithms, intuitionistic logic are considered. These theories are simplified substantially with the postulate that the objects they consider are independent of (have small mutual information with) any sequence specified by a mathematical property.
307 citations
TL;DR: It is proved that, even if the clocks all run at the same rate as real time and there are no failures, an uncertainty of e in the message delivery time makes it impossible to synchronize the clocks of n processes any more closely than e(1−1/ n ).
Abstract: The problem of synchronizing clocks of processes in a fully connected network is considered. It is proved that, even if the clocks all run at the same rate as real time and there are no failures, an uncertainty of e in the message delivery time makes it impossible to synchronize the clocks of n processes any more closely than e(1−1/ n ). A simple algorithm is given that achieves this bound.
266 citations
TL;DR: The main result is characterizing a large class of graph properties for which the respective “succinct problem” is NP-hard, and shows that the succinct versions of polynomially equivalent problems may not be polynomial equivalent.
Abstract: For a fixed graph property Q , the complexity of the problem: Given a graph G , does G have property Q ? is usually investigated as a function of | V |, the number of vertices in G , with the assumption that the input size is polynomial in | V |. In this paper the complexity of these problems is investigated when the input graph is given by a succinct representation. By a succinct representation it is meant that the input size is polylog in | V |. It is shown that graph problems which are approached this way become intractable. Actually, no “nontrivial” problem could be found which can be solved in polynomial time. The main result is characterizing a large class of graph properties for which the respective “succinct problem” is NP-hard. Trying to locate these problems within the P-Time hierarchy shows that the succinct versions of polynomially equivalent problems may not be polynomially equivalent.
260 citations
TL;DR: The method introduces a generalization of the ring of integers, called well-endowed rings, which possesses a very efficient parallel implementation of the basic (+,−,×) ring operations.
Abstract: It is shown that a probabilistic Turing acceptor or transducer running within space bound S can be simulated by a time S2 parallel machine and therefore by a space S2 deterministic machine. (Previous simulations ran in space S6.) In order to achieve these simulations, known algorithms are extended for the computation of determinants in small arithmetic parallel time to computations having small Boolean parallel time, and this development is applied to computing the completion of stochastic matrices. The method introduces a generalization of the ring of integers, called well-endowed rings. Such rings possess a very efficient parallel implementation of the basic (+,−,×) ring operations.
173 citations
TL;DR: A simple observation shows that both implication problems are recursively unsolvable, and it follows that there is noRecursively enumerable set of axioms for finite implication.
Abstract: There are two implication problems for functional dependencies and inclusion dependencies: general implication and finite implication. Given a set of dependencies Σ ∪ { σ }, the problems are to determine whether σ holds in all databases satisfying Σ or all finite databases satisfying Σ . Contrary to the possibility suggested in Casanova, Fagin, and Papadimitriou (“Proceedings, 1st ACM Conf. on Principles of Database System,” pp. 171–176, 1982), there is a natural, complete axiom system for general implication. However, a simple observation shows that both implication problems are recursively unsolvable. It follows that there is no recursively enumerable set of axioms for finite implication.
142 citations
TL;DR: The complexity of uniform word problems for commutative grammars is investigated and various classes of commutatives are defined.
Abstract: Commutative grammars are introduced, and various classes of commutative grammars are defined. The complexity of uniform word problems for commutative grammars is investigated.
77 citations
TL;DR: It appears that for a wide class of statistics on trees, pattern-matching has a linear expected time complexity (in contrast to a quadratic worst-case behaviour).
Abstract: This paper presents general results on the probabilities of occurrences of patterns in trees, which serve to analyze a commonly used pattern matching algorithm on trees. It appears that for a wide class of statistics on trees, pattern-matching has a linear expected time complexity (in contrast to a quadratic worst-case behaviour). The methods used are both combinatorial and analytic and prove useful in the evaluation of a wide class of tree algorithms.
74 citations
TL;DR: The computational complexity of the solution y of the differential equation y ′( x ) = f ( x, y ( x )), with the initial value y (0) = 0, relative to the computational complex of the function f is investigated and the Lipschitz condition is shown to play an important role.
Abstract: The computational complexity of the solution y of the differential equation y ′( x ) = f ( x, y ( x )), with the initial value y (0) = 0, relative to the computational complexity of the function f is investigated. The Lipschitz condition on the function f is shown to play an important role in this problem. On the one hand, examples are given in which f is polynomial time computable but none of the solutions y is computable. On the other hand, if f is polynomial time computable and if f satisfies a weak form of the Lipschitz condition then the (unique) solution y is polynomial space computable. Furthermore, there exists a polynomial time computable function f which satisfies this weak Lipschitz condition such that the (unique) solution y is not polynomial time computable unless P = PSPACE.
TL;DR: A subclass of Petri nets called live and safe free choice nets (LSFC nets) is studied and it is shown that the restricted combination of concurrency and choice as represented by LSFC nets leads to a number of attractive system properties.
Abstract: A subclass of Petri nets called live and safe free choice nets (LSFC nets) is studied. LSFC nets model distributed systems that can exhibit both nonsequential and nondeterministic behaviours. It is shown that the restricted combination of concurrency and choice as represented by LSFC nets leads to a number of attractive system properties. It is also shown, through examples, that a “less” restrictive combination of concurrency and choice destroys these properties.
TL;DR: The proof shows that when a polyomino P tessellates the plane without rotations or reflections, then it can tessellingate the plane periodically, i.e., with the instances of P arranged in a lattice.
Abstract: Given N distinct memory modules, the elements of an (infinite) array in storage are distributed such that any set of N elements arranged according to a given data template T can be accessed rapidly in parallel. Array embeddings that allow for this are called skewing schemes and have been studied in connection with vector processing and SIMD machines. In 1975 Shapiro (IEEE Trans. Comput. C-27 (1978), 421–428) proved that there exists a valid skewing scheme for a template T if and only if T tessellates the plane. A conjecture of Shapiro is settled and it is proved that for polyominos P a valid skewing scheme exists if and only if there exists a valid periodic skewing scheme. (Periodicity implies a rapid technique to locate data elements.) The proof shows that when a polyomino P tessellates the plane without rotations or reflections, then it can tessellate the plane periodically, i.e., with the instances of P arranged in a lattice. It is also proved that there is a polynomial time algorithm to decide whether a polyomino tessellates the plane, assuming the polyominos in the tessellation should all have an equal orientation.
TL;DR: Two counterexamples to the random oracle hypothesis as formalized by Bennett and Gill are given and it is believed that these examples will severely test any new candidate for a formal random oracles hypothesis.
Abstract: Two counterexamples to the random oracle hypothesis as formalized by Bennett and Gill (1975, SIAM J. Comput. 10 , 96–113), are given. Then the future of the random oracle hypothesis in light of these examples is discussed. It is believed that these examples will severely test any new candidate for a formal random oracle hypothesis.
TL;DR: This note presents an extended first-order logic designed to be exactly equivalent in expressiveness to polynomialsize, constant-depth, unbounded-fan-in circuits constructed by Turing machines of bounded computational complexity.
Abstract: Consider a family of boolean circuits C~, C2,..., C,,..., constructed by some uniform, effective procedure operating on input n. Such a procedure provides a concise representation of a family of parallel algorithms for computing boolean values. A formula of first-order logic may also be viewed as a concise representation of a family of parallel algorithms for evaluating boolean functions. The parallelism is implicit in the quantification (a formula gx q~(x) is true if and only if each of the formulas q~(a) is true, and all these formulas can be checked simultaneously), and universes of different sizes give rise to boolean functions with different numbers of inputs (the boolean values of the formula's predicates on various combinations of elements of the universe). This note presents an extended first-order logic designed to be exactly equivalent in expressiveness to polynomialsize, constant-depth, unbounded-fan-in circuits constructed by Turing machines of bounded computational complexity. © 1984 Academic Press, Inc.
TL;DR: A language for processes is defined in which there are two methods of synchronising subprocesses called loose synchronisation and tight synchronisation, and it is proved that there exists a fully abstract model in the sense of Scott.
Abstract: A language for processes is defined in which there are two methods of synchronising subprocesses called loose synchronisation and tight synchronisation. A notion of experimenting on processes is introduced which leads to definitions of when a process may pass an experiment and when it must pass an experiment. By connecting the experimenter to the process using the tight synchronisation then three preorders on processes called the synchronous preorders are defined. By using the loose synchronisation primitive, the asynchronous preorders are defined. For each of these preorders it is proved that there exists a fully abstract model in the sense of Scott. These models are defined using sets of equations and lead automatically to complete proof systems. Moreover the proof of full abstractness uses an alternative characterisation of these preorders which gives an intuitive understanding for the denotations in the model.
TL;DR: A novel sorting algorithm for unidirectional rings achieves the first lower bound in a distributed system of N processors.
Abstract: The sorting problem is to arrange N values in a distributed system of N processors into sorted order. Let the values be in {0,…, L }. Every sorting algorithm requires Ω( N 2 lg( L/N )/lg N ) messages on a bidirectional ring with N processors. Every sorting algorithm requires Ω( N 3/2 lg( L/N )/lg N ) messages on a square mesh with N processors. A novel sorting algorithm for unidirectional rings achieves the first lower bound.
TL;DR: The expected number of interchanges and comparisons in Floyd's well-known algorithm to construct heaps and derive the probability generating functions for these quantities are considered.
Abstract: The expected number of interchanges and comparisons in Floyd's well-known algorithm to construct heaps and derive the probability generating functions for these quantities are considered. From these functions the corresponding expected values are computed.
TL;DR: Efficient algorithms for the construction of optimal decision trees and optimal one-time-only branching programs for symmetric Boolean functions are presented and an exponential lower bound on the decision tree complexity of some Boolean function is shown having linear formula size.
Abstract: Combinational complexity and depth are the most important complexity measures for Boolean functions. It has turned out to be very hard to prove good lower bounds on the combinational complexity or the depth of explicitly defined Boolean functions. Therefore one has restricted oneself to models where nontrivial lower bounds are easier to prove. Here decision trees, branching programs, and one-time-only branching programs are considered, where each variable may be tested on each path of computation only once. Efficient algorithms for the construction of optimal decision trees and optimal one-time-only branching programs for symmetric Boolean functions are presented. Furthermore, the following trade-off results are proved. An exponential lower bound on the decision tree complexity of some Boolean function is shown having linear formula size and linear one-time-only branching program complexity. Furthermore, a quadratic lower bound on the one-time-only branching program complexity of some Boolean function is shown having linear combinational complexity.
TL;DR: A connection is established between the semantic theories of concurrency and communication in the works of de Bakker and Zucker and Milner, who develop an algebraic semantics of communication based upon observational equivalence between processes.
Abstract: A connection is established between the semantic theories of concurrency and communication in the works of de Bakker and Zucker, who develop a denotational semantics of concurrency using metric spaces instead of complete partial orders, and Milner, who develops an algebraic semantics of communication based upon observational equivalence between processes. His rigid synchronization trees (RSTs) are endowed with a simple pseudometric distance induced by Milner's weak equivalence relation and the quotient space is shown to be complete. An isometry between this space and the solution to a domain equation of de Bakker and Zucker is established, presenting their solution in a conceptually simpler framework. Under an additional assumption, the equivalence between the weak equivalence relation over RSTs and the elementary equivalence relation induced by the sentences of a modal logic due to Hennessy and Milner is established.
TL;DR: Generalized Horn clauses (GHC) are introduced through an informal description of their operational semantics, which allows discussion of some typical synchronization problems and is proved equivalent to GHC.
Abstract: An extension of Horn clause logic is defined based on the introduction of a synchronization operator. Generalized Horn clauses (GHC) are introduced through an informal description of their operational semantics, which allows discussion of some typical synchronization problems. GHC are first considered formally as a programming language by defining the syntax, the operational semantics, the model-theoretic semantics, and the fixed-point semantics. The above mentioned semantics are given in the Van Emden-Kowalski style (1976, J. Assoc. Comput. Mach. 23, 733–742) and are proved equivalent. GHC are then characterized as axiomatic theories. A set of axiom schemata concerned with the newly introduced synchronization operator is defined and it is proved that the operational semantics inference rule is both sound and complete. Finally, the relation between GHC and Horn clauses is analyzed, and it is proved that Horn clause logic is strictly included in the generalized Horn clause logic.
TL;DR: A sequence of dynamic logics of increasing expressive power, which correspond, over appropriate finite structures, to LOGSPACE, PTIME, and PSPACE, as well as to the sets definable in the logarithmic-space, polynomial-time, and arithmetical hierarchies is exhibited.
Abstract: Several versions of quantified dynamic logic are shown to be equivalent in expressive power to “static” extensions of classical logics. Consequently, by recent results of various researchers, many connections between dynamic logics and complexity classes are obtained. Among other things, a sequence of dynamic logics of increasing expressive power, which correspond, over appropriate finite structures, to LOGSPACE, PTIME, and PSPACE, as well as to the sets definable in the logarithmic-space, polynomial-time, and arithmetical hierarchies is exhibited.
TL;DR: A protocol is given which deals cards to three or more players in a fair way and some related questions are also discussed.
Abstract: A protocol is given which deals cards to three or more players in a fair way. Some related questions are also discussed.
TL;DR: This paper exhibits a-class of AT2-optimal multipliers with computation times [Ω(logn), 0(n1/2]], based on the DFT on a Fermat ring, whose elements are represented in a redundant radix-4 form to ensure 0(1) addition time.
Abstract: According to VLSI theory, [logn, √n] is the range of computation times for which there may exist an AT2-optimal multiplier of n-bit integers. Such networks were previously known for the time range [Ω(log2n), 0(√n)]; in this paper we settle this theoretical question, by exhibiting a-class of AT2-optimal multipliers with computation times [Ω(logn), 0(n1/2)]. Our designs are based on the DFT on a Fermat ring, whose elements are represented in a redundant radix-4 form to ensure 0(1) addition time.
TL;DR: It is shown that it is decidable whether an arbitrary DOL language is repetitive and it is also shown that if a DOLlanguage is repetitive then it is strongly repetitive.
Abstract: A language K ⊆ Σ * is repetitive if for each positive integer n there exists a word w ∈ Σ + such that w n is a subword of K . Language K is called strongly repetitive if there exists a word w ∈ Σ + , such that, for each positive integer n , w n is a subword of K . It is shown that it is decidable whether an arbitrary DOL language is repetitive. It is also shown that if a DOL language is repetitive then it is strongly repetitive.
TL;DR: The satisfiability problem for a class of proportional sentences is considered and it is proposed that a new inference rule, based on the resolution principle, by which (un)satisfiability for S 0 in polynomial time can be decided.
Abstract: In this paper, the satisfiability problem for a class of proportional sentences is considered. Here a sentence is a set of clauses. A clause is a set of literals. First, it is proposed that a class S 0 of propositional sentences which properly includes the class of propositional Horn sentences. A sentence { C 1 ,…, C n } is in S 0 if there are sets P 1 ,…, P n of positive literals such that (1) P 1 ⊃ P 2 ⊃ … ⊃ P n , (2) P i C i for 1 ⩽ i ⩽ n , and (3) C i − P i is a Horn clause for 1 ⩽ i ⩽ n . Then it is proposed that a new inference rule, based on the resolution principle, by which (un)satisfiability for S 0 in polynomial time can be decided.
TL;DR: This paper deals with the simple but sufficiently powerful applicative language (λ-calculus) and studies effectiveness properties of its semantics and analyses the effectiveness of the interpretation of λ-terms as well as different notions of computability over models.
Abstract: The syntax of a formal language is effectively given. This is not immediately so for the semantics. This paper deals with the simple but sufficiently powerful applicative language (λ-calculus) and studies effectiveness properties of its semantics. In particular it analyses the effectiveness of the interpretation of λ-terms as well as different notions of computability over models.
TL;DR: It is proved that the well-known computational models RAM, vector machines, Turing machines, uniform circuits, uniform aggregates, storage modification Machines, hardware modification machines,…, are all similar in the sense that their parallel time, their sequential time, and their space complexities are polynomially related simultaneously.
Abstract: This paper describes what is the parallel time for sequential models, what is the sequential time for parallel models, and proves that the well-known computational models RAM, vector machines, Turing machines, uniform circuits, uniform aggregates, storage modification machines, hardware modification machines,…, are all similar in the sense that their parallel time, their sequential time, and their space complexities are polynomially related simultaneously.
TL;DR: The semantics of a simple language for describing tightly coupled “synchronous” systems is defined and a consistent fully abstract denotational semantics is defined based on the concept of observable behavior and advanced fixed point theory.
Abstract: The semantics of a simple language for describing tightly coupled “synchronous” systems is defined. An operational semantics is given by term rewriting rules and a consistent fully abstract denotational semantics is defined based on the concept of observable behavior and advanced fixed point theory. Particular properties of the language are analysed and especially algebraic laws of the language are discussed. Finally some aspects and problems of the formal definition of the semantics of such a language are treated also comparing them to other approaches found in the literature.
TL;DR: The following lower bounds for on-line computation are proved: Simulating two-tape nondeterministic machines by one-Tape machines requires Ω(n log n) time.
Abstract: The following lower bounds for on-line computation are proved: (1) Simulating two-tape nondeterministic machines by one-tape machines requires Ω(n log n) time. (2) Simulating k-tape (deterministic) machines by machines with k-pushdown stores requires Ω(n log1/(k+1)n) time.