- Email: [email protected]
Computational semantics of terms rewriting systems
both textual and relational data. In this approach the user sees two distinct data bases that (s)he can declare and query. Text interpretation and Text generation mappings allow the user to view his(her) data as (s)he wishes. We define a Text Definition Language (TDL) which is simply based on regular expressions and a Text Query Language (TQL) that is a calculus-oriented Text language based on the notion of cursors. The language is both defined informally through simple examples and formally through painful mathematics (INRIA Researcn Report No. 145).
The Complexity of Generating an Exponentially Distributed Variate by Ph. Flajolet and N. Saheb We analyze in detail an almost optimal algorithm for generating an exponentially distributed variate. The algorithm is due to Knuth and Yao and relies on a method which goes back to J. Von Neumann. It is shown that it can generate k bits of an exponentially distributed variate using an average of about k+5.67974692 coin flippings. This solves a problem left open by Knuth and Yao (INRIA Research Report No. 159).
Compiling Relational Queries for a Finite State Automaton Hardware Filter
questions related to the magnetohydrodynamic equations (MHD equations) for a viscous incompressible resistive fluid. Most of the questions which we investigate are related to the large time behaviour of the solutions, and the results tend to show that, for large times (i.e. after some transient period), if the dimension of space is N = 2, the flow is totally determined by a finite number of parameters. The same results hold also if the dimension of space is three, unless singularities in the sense of J. Leray develop in three-dimensional flows (INRIA Research Report No. 185).
Computational Semantics of Terms Rewriting Systems by G. Boudol We study the structure of computations by term rewrite rules, allowing non-determinism and overlapping. Computations form, up to permutations of rewritings, a complete partial order, and semantics is defined as the set of results of terminating (i.e. maximal) computations. A call-by-need computation rule is then introduced and we prove, by means of a continuous projection over the complete partial order of call-by-need computations, that it is correct for sequential systems (INRIA Research Report No. 192).
An Improved Algorithm for Hierarchical Clustering Using Strong Components by Robert E. Tarjan
by D. Plateau Most data base machines use a hardware filter that performs the projection and selection operation on the fly during disk transfer. Many possible designs have been proposed for such filters and a promising approach seems to be to use a finite state automaton. In this paper we briefly describe such a filter and we present an algorithm that compiles selection/projection queries into finite state automata (FSA). A major drawback of the approach is the size of the FSA, therefore we give an evaluation of the number of states of the automaton (INRIA Research Report No. 171).
Some Mathematical Questions Related to the MHD Equations by M. Sermange and R. Temam The purpose of this article is to study some 212
In 1582 the author presented an O(m(Iog n) 2) time algorithm for hierarchically decomposing a directed n-vertex, m-edge graph with weighted edges into strong components. Such an algorithm is useful in cluster analysis of data with an asymmetric similarity measure. The present paper gives a simpler algorithm with the faster running time of O(m log n) (Information ProcessingLetters 17, 1 (1983)).
Log-Logarithmic WorstCase Range Queries Are Possible in Space E)(N) Dan E. Willard Let S denote a set of N records whose keys are distinct nonnegative integers less than some initially specified bound M. This paper introduces a new data structure, called the yf i s t trie, which uses E)(N) space and E)(Iog log M) time for range queries on a random access
machine. We will also define a simpler but less efficient structure, called the x-fast trie (Information Processing Letters 17, 2 (1983)).
A Faster Algorithm for Finding Edge-Disjoint Branchings Po Tong and E.L. Lawler An O(k 2 mn) algorithm is proposed for finding k edge-disjoint branchings in a directed multigraph with m edges and n vertices. With appropriate preprocessing the time bound can be reduced to O(kmn + k3n2). Our proposed algorithm runs faster than any previously known algorithm and provides yet another constructive proof of Edmonds' Bronchings Theorem (Information Processing Letters 17, 2 (1983)).
On the Arithmetic Complexity of Matrix Kronecker Powers by Gadie/ Seroussi and Fai Ma In this paper we study the arithmetic complexity of computing the pth Kronecker power of an n x n matrix. We first analyze a straightforward inductive computation which requires an asymptotic average of p multiplications and p-1 additions per computed output. We then apply efficient methods for matrix multiplication to obtain an algorithm that achieves the optimal rate of one multiplication per output at the expense of increasing the number of additions, and an algorithm that requires O(Iog p) multiplications and O(Iog 2p) additions per output (Information Processing Letters 17, 3 (1983)).
Where Oblivious is not Sufficient by Reiner Kolla Lipton and Sedgewick have made some generalisations of Thompson's VLSI-model by weakening some restrictions about the input-output schedule (where-oblivious, when-oblivious). They claim that the lower bound results for Thompson's model hold under the assumption that the i/o schedule is where-oblivious and that using their proof-technique they could prove similar bounds for a numbe r of problems. In this paper we show that this is not correct, but it holds under a stronger restriction which is given here (strongly where-oblivious) (Information Processing Letters 17, 4 (1983)).
The Complexity of Generating an Exponentially Distributed Variate by Ph. Flajolet and N. Saheb We analyze in detail an almost optimal algorithm for generating an exponentially distributed variate. The algorithm is due to Knuth and Yao and relies on a method which goes back to J. Von Neumann. It is shown that it can generate k bits of an exponentially distributed variate using an average of about k+5.67974692 coin flippings. This solves a problem left open by Knuth and Yao (INRIA Research Report No. 159).
Compiling Relational Queries for a Finite State Automaton Hardware Filter
questions related to the magnetohydrodynamic equations (MHD equations) for a viscous incompressible resistive fluid. Most of the questions which we investigate are related to the large time behaviour of the solutions, and the results tend to show that, for large times (i.e. after some transient period), if the dimension of space is N = 2, the flow is totally determined by a finite number of parameters. The same results hold also if the dimension of space is three, unless singularities in the sense of J. Leray develop in three-dimensional flows (INRIA Research Report No. 185).
Computational Semantics of Terms Rewriting Systems by G. Boudol We study the structure of computations by term rewrite rules, allowing non-determinism and overlapping. Computations form, up to permutations of rewritings, a complete partial order, and semantics is defined as the set of results of terminating (i.e. maximal) computations. A call-by-need computation rule is then introduced and we prove, by means of a continuous projection over the complete partial order of call-by-need computations, that it is correct for sequential systems (INRIA Research Report No. 192).
An Improved Algorithm for Hierarchical Clustering Using Strong Components by Robert E. Tarjan
by D. Plateau Most data base machines use a hardware filter that performs the projection and selection operation on the fly during disk transfer. Many possible designs have been proposed for such filters and a promising approach seems to be to use a finite state automaton. In this paper we briefly describe such a filter and we present an algorithm that compiles selection/projection queries into finite state automata (FSA). A major drawback of the approach is the size of the FSA, therefore we give an evaluation of the number of states of the automaton (INRIA Research Report No. 171).
Some Mathematical Questions Related to the MHD Equations by M. Sermange and R. Temam The purpose of this article is to study some 212
In 1582 the author presented an O(m(Iog n) 2) time algorithm for hierarchically decomposing a directed n-vertex, m-edge graph with weighted edges into strong components. Such an algorithm is useful in cluster analysis of data with an asymmetric similarity measure. The present paper gives a simpler algorithm with the faster running time of O(m log n) (Information ProcessingLetters 17, 1 (1983)).
Log-Logarithmic WorstCase Range Queries Are Possible in Space E)(N) Dan E. Willard Let S denote a set of N records whose keys are distinct nonnegative integers less than some initially specified bound M. This paper introduces a new data structure, called the yf i s t trie, which uses E)(N) space and E)(Iog log M) time for range queries on a random access
machine. We will also define a simpler but less efficient structure, called the x-fast trie (Information Processing Letters 17, 2 (1983)).
A Faster Algorithm for Finding Edge-Disjoint Branchings Po Tong and E.L. Lawler An O(k 2 mn) algorithm is proposed for finding k edge-disjoint branchings in a directed multigraph with m edges and n vertices. With appropriate preprocessing the time bound can be reduced to O(kmn + k3n2). Our proposed algorithm runs faster than any previously known algorithm and provides yet another constructive proof of Edmonds' Bronchings Theorem (Information Processing Letters 17, 2 (1983)).
On the Arithmetic Complexity of Matrix Kronecker Powers by Gadie/ Seroussi and Fai Ma In this paper we study the arithmetic complexity of computing the pth Kronecker power of an n x n matrix. We first analyze a straightforward inductive computation which requires an asymptotic average of p multiplications and p-1 additions per computed output. We then apply efficient methods for matrix multiplication to obtain an algorithm that achieves the optimal rate of one multiplication per output at the expense of increasing the number of additions, and an algorithm that requires O(Iog p) multiplications and O(Iog 2p) additions per output (Information Processing Letters 17, 3 (1983)).
Where Oblivious is not Sufficient by Reiner Kolla Lipton and Sedgewick have made some generalisations of Thompson's VLSI-model by weakening some restrictions about the input-output schedule (where-oblivious, when-oblivious). They claim that the lower bound results for Thompson's model hold under the assumption that the i/o schedule is where-oblivious and that using their proof-technique they could prove similar bounds for a numbe r of problems. In this paper we show that this is not correct, but it holds under a stronger restriction which is given here (strongly where-oblivious) (Information Processing Letters 17, 4 (1983)).