This paper is devoted to the study of occurrence nets as models of non-sequential processes, and of some of their properties. We characterise the properties known as discreteness, K-density and D-continuity which have been proposed in the literature as meaningful properties of processes. We show that they are closely related to each other.
We consider parallel computers (PC's) with fixed communication network with bounded degree. We construct a universal PC with n1+0(1/log log (n)) processors which can simulate each PC with n prodessors with a time loss of 0(log log(n)). This improves a result of [1] where a time loss of 0(log (n)) was achieved but only using 0(n) processors. Furthermore we prove a time-processor trade-off for a very general type of universal PC's, which includes thatone above. This generalizes a result for a simpler type of simulations presented in [2], where also all results of this paper are included.
We present an algorithm which will factor an integer n quite efficiently if the class number h ( − n ) h( - n) is free of large prime divisors. The running time T ( n ) T(n) (number of compositions in the class group) satisfies prob [ T ( m ) ⩽ n 1 / 2 r ] ≳ ( r − 2 ) − ( r − 2 ) \operatorname {prob}[T(m) \leqslant {n^{1/2r}}] \gtrsim {(r - 2)^{ - (r - 2)}} for random m ∈ [ n / 2 , n ] m \in [n/2,n] and r ⩾ 2 r \geqslant 2 . So far it is unpredictable which numbers will be factored fast. Running the algorithm on all discriminants - ns with s ⩽ r r s \leqslant {r^r} and r = ln n / ln ln n r = \sqrt {\ln n/\ln \ln n} , every composite integer n will be factored in o ( exp ln n ln ln n ) o(\exp \sqrt {\ln n\ln \ln n} ) bit operations. The method requires an amount of storage space which is proportional to the length of the input n. In our analysis we assume a lower bound on the frequency of class numbers h ( − m ) h( - m) , m ⩽ n m \leqslant n , which are free of large prime divisors.
A hierarchy of sets of infinite (valued) trees is introduced which has no counterpart in the theory of sets of infinite strings ("ω-languages"). As a consequence we obtain that for sets of infinite trees an analogue of McNaughton's fundamental theorem on ω-languages does not hold.
Here is introduced an extension for infinite words of the classical notion of rational transduction. We prove that this extension has the important property of mapping the adherence of a language of finite words into the adherence of an other language of finite words. The set of such extensions is closed by composition and is exactly the family of the compositions of an inverse faithful sequential mapping and of a faithful sequential mapping.
We introduce a new model of parallel computation, namely the FIFO nets. First, we introduce some basic definitions. A restriction of this model has the power of the Turing machine. Monogeneous Fifo nets are then introduced. The coverability tree is a procedure to decide whether a monogeneous net is bounded or not. At last, regularity is decidable for monogeneous nets.
The paper proposes an axiomatic approach to semantics of specification languages. It introduces the notion of a semantical system as a framework to discuss and compare various approaches to specification of (algebraic) data types and to spell out their underlying assumptions. For various of those assumptions we present complete specification languages or show that existing specification languages are complete. Initial and final semantics are characterized as special cases of our unifying concept of semantical systems which admit D-free structures.
In the past years there have been many attempts to fill in the gap between the classes of LL(k) and LR(k) grammars with new classes of deterministically parsable grammars. Almost always the introduction of a new class was accompanied by a parsing method and/or a grammatical transformation fitting the following scheme. If parsers were at the centre of the investigation the new method used to be designed to possess certain advantages with respect to already existing ones. As far as transformations were concerned the intention was to produce methods of transforming grammars into more easily parsable ones. The problem of finding classes of context-free grammars which can be transformed to LL(k) grammars has received much attention. Parsing strategies and associated classes of grammars generating LL(k) languages have been extensively studied. An equally interesting class of grammars is the class of strict deterministic grammars, a subclass of the LR(O) grammars with elegant theoretical properties. Generalizations of this concept have been introduced by Friede and Pittl. The purpose of this paper is to show how the above mentioned classes of grammars can be dealt with within a general framework.
Problems of optimally partitioning complex figures into simpler figures belong to the kernel of computational geometry. Besides inherent applications to computational geometry [C80], they have a variety of applications in pattern recognition [OS82], numerical analysis, database systems [LLMPL79], VLSI and arc~tecture design [LPRS82]. In design problems, minimiT.ation of the total length of edges of the simpler figures may be more important. In [LPRS82], the following problem has been investigated:
We give a unified framework to treat the following problem. Let (L_1, ..., L_n) → f(L_1, ..., L_n) be an operation on languages. Given monoids recognizing the languages L_1, ..., L_n, give an explicit construction of a monoid recognizing f(L_1, ..., L_n). Our method gives in particular a simple way to prove that an operation preserves rational languages. The scope of our method is quite broad and goes from classical operations such as union, intersection, concatenation, quotient, shuffle, inverse and direct morphisms, etc., to less classical ones such as infiltration, Dyck reduction, longest common prefix, Straubing's counting, etc. It includes also questions that are not expressed directly as operations on languages, as, for example, Reutenauer's theorem on TOL-systems. The key idea of our construction is to consider an operation as the inverse of a transduction.
Furthermore, asymptotic equivalents for these expected values and exact expressions for the higher moments about the origin are computed.
The problem of deciding whether an axiomatic specification of an abstract data type is sufficiently-complete is known to be in general unsolvable. Regarding axioms as directed rewrite rules instead of symmetric equations a specification defines a reduction relation on terms. It is proved that in the subclass of left-linear axiomatic specifications the property of sufficient-completeness is decidable, if the corresponding reduction relation is normalizing and confluent. The presented algorithm can also be used to determine a set of constructors for a specified data type.
On montre que le mot de Morse est le seul mot infini sans chevauchement sur un alphabet à deux lettres que l'on puisse obtenir par itération d'un morphisme. De plus, on montre que si un mot infini, formé des mêmes facteurs que le mot de Fibonacci, est obtenu par itération d'un morphisme, ce morphisme appartient au demi-groupe engendré par deux morphismes particuliers.
The specification of abstract data types requires the possibility to treat exceptions and errors. We present an approach allowing all forms of error handling : error introduction, error propagation and error recovery. The algebraic semantics Of our method and a new correctness criterion is given. We also introduce an operational semantics of a subclass of our specifications which coincides with the algebraic semantics.
