V. Diekert and G. Rozenberg (Eds.) The Book of Traces. World Scientific, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of systems of high abstraction. Since trace monoids are a generalization of free monoids, it was tempting to extend the investigation of free monoids to free partially commutative monoids. This resulted, e.g. in the extensive consideration of recognizable and rational trace languages (cf. [18] for a collection of surveys on this field) trace equations [20, 44, 17] and trace rewriting systems [15, 16, 38 40] Our main result states that for any finite trace rewriting system, the first order theory of the associated one step rewrite graph is decidable. Because of the non local effects ....

....5 if evaluates to true in 5 . Finally the first order theory of 5 denotes the set of all first order sentences over the signature of 5 with 5 . 3 Rewriting in trace monoids 3. 1 Trace monoids and recognizable trace languages In the following we introduce some notions from trace theory, see [18] for more details. An independence relation on an alphabet is an irreflexive and symmetric relation , the complementary relation is called a dependence relation. The pair (resp. is called an independence alphabet (resp. a dependence alphabet) Given an ....

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....in 1969 by Cartier and Foata [11] as a tool for the study of Mobius functions. In the following decades trace monoids appeared in connection with different research fields and a self contained theory of traces has also gradually developed. Finally, in 1995 the first monograph on trace theory [18] was published, presenting an overview of various directions of research on partial commutativity, and two years later one chapter of the Handbook of Formal Languages [15] was devoted exclusively to trace monoids. Topics considered in the framework of trace theory belong to many areas of both ....

V. Diekert, G. Rozenberg (Eds.), The Book of Traces, World Scientific, Singapore, 1995.

....monoid whose independence graph is the ladder graph. Keywords: Automata and formal languages, trace monoids, CartierFoata normal form, height function, generating series, speedup, performance evaluation. 1 Introduction Traces are used to model the occurrence of events in concurrent systems [12]. Roughly speaking, a letter corresponds to an event and two letters commute when the corresponding events can occur simultaneously. In this context, the two basic performance measures associated with a trace t are its length jtj (the sequential execution time) and its height h(t) the ....

....#ft 2 M ; h(t) ng Gamma fl M : Furthermore, the numbers M and fl M are algebraic. Explicit formulas involving the series L and H are given for M and fl M . 2 The Trace Monoid We start by introducing all the necessary notions from the theory of trace monoids. The reader may refer to [11, 12] for further information. In the sequel, a graph is a couple (N; A) where N is a finite non empty set and A ae N Theta N . Hence we consider directed graphs, allowing for selfloops but not multi arcs. Dependence graphs and independence graphs (to be defined below) which are naturally ....

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapour, 1995.

....for K 1 = K 2 this implies the decidability of K 1 = K 2 . 2 3 Language theoretic applications Let Sigma be a finite alphabet and let I Sigma Theta Sigma be an irreflexive and symmetric relation on Sigma. Denote by M ( Sigma; I) the associated trace monoid (see Diekert and Rozenberg [3]) and let OE : Sigma Gamma M ( Sigma; I) be the canonical morphism. If Delta Sigma is nonempty, let pr Delta : Sigma Gamma Delta be the projection mapping defined by pr Delta (oe) oe if oe 2 Delta and pr Delta (oe) otherwise. Then for w 1 ; w 2 2 Sigma we have OE(w ....

....applicable to D0L (resp. DT0L, HDT0L) subsets of trace monoids. The following results are more general. Note that, in general, if g : Sigma Gamma Sigma is a morphism there does not exist a morphism h : M ( Sigma; I) Gamma M ( Sigma; I) such that OEg = hOE (see Diekert and Rozenberg [3]) 5 are HDT0L sets of Sigma , it is decidable whether or not K 1 and K 2 are strongly equivalent inside M ( Sigma; I) i.e. whether or not OEhh i 1 h i 2 : h i k (w 1 ) OEgg i 1 g i 2 : g i k (w 2 ) for all k 0, 1 i 1 ; i k s. Proof. The claim follows by ....

V. Diekert and G. Rozenberg (eds.), The Book of Traces, World Scientific, Singapore, 1995.

.... within an interleaving model (under some assumptions that effectively require that the refinement of actions respects their dependencies) The idea of action dependencies regulating orderings has been suggested and inten sively studied by Mazurkiewicz [55, 56, 57] and others (see for instance [30]) The basic concept in Mazurkiewicz work are traces, which are equivalence classes of sequences of actions, factorised by a permutation equivalence: in a sequence, adjacent independent actions may be commuted. System behaviour is described as a set of traces, constituting the possible runs of ....

....term B b is the transition system Its(B) L, B) where is the smallest set of transitions agreeing with the rules in Tables 2 and 3. Note that, in the presence of a dependency relation D C Act x Act, it is often required that transition systems satisfy some diamond closure properties (see [30]) e.g. for all a I b 1. if s s s , then s s s for some s; 2. if s s and s s , then s s and s s for some s. The transition systems generated by our operational semantics satisfy neither of the above properties; the first, however, can be recaptured as soon as we interpret ....

[Article contains additional citation context not shown here]

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, 1995.

....order semantics; Semiwords; Semi languages; Algorithms. 1. Introduction Partial order semantics of formalisms designed to describe concurrent systems have a long history (approximately 30 years) Concentrating on Petri nets, instances of those semantics are processes [2] Mazurkiewicz traces [14, 6], partially ordered multisets (pomsets) 18] prime) event structures [17] partial words [10] and semiwords [20, 26] or branching processes [7] the list is far from being complete) Especially a finite representation of a branching process of a 1 bounded Petri net, called the finite prefix of ....

V. DIEKERT AND G. ROZENBERG, The Book of Traces, World Scientific, 1995.

....of computation. Yet another motivation for focussing on regularity is that the classical notion of a regular collection of objects has turned out to be very fruitful in a variety of settings including finite (and infinite) strings, trees and restricted partial orders known as Mazurkiewicz traces [8, 23, 24]. In all these settings there is a representation of regular collections in terms of finite state devices. There is also an accompanying monadic second order logic which usually induces temporal logics using which one can reason about such collections [23] One can then develop automated ....

....MSC language is finitely generated. Following this, we establish that the class of finitely generated regular MSC languages coincides with the class of languages defined by locally synchronized MSGs. In one direction, this characterization hinges crucially on elements of Mazurkiewicz trace theory [8, 26]. In this paper we confine our attention to finite MSCs. We feel however that our results will serve as a good launching pad for a similar account concerning infinite MSCs. This should then lead to the design of appropriate temporal logics and automata theoretic solutions (based on ....

[Article contains additional citation context not shown here]

Diekert, V., Rozenberg, G. (Eds.): The Book of Traces. World Scientific (1995)

.... P (process line ordering) In general, the visual order provides more ordering than intended by the designer. Therefore every chart has an associated causal structure providing the intended ordering [1] Causal structures are related to pomsets [9] event structures [8] and Mazurkiewicz traces [4]. A causal structure is obtained from a chart by means of a given semantics, which depends on the system architecture. Formally, the causal structure of a chart M = E ; P ; L; T ) is given as tr(M) E ; OE; P ; L; T ) where the only difference between M and tr(M) is the poset (E ; OE) with ....

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....below, a mapping : M ( Sigma; D) S is asynchronous if it can be computed stepwise in a distributed way, thus being easily transformed into an equivalent deterministic asynchronous (cellular) automaton. For more details and general notions on traces and asynchronous automata see Ch. 7,8 in [7]. Before recalling the definition, let us introduce a basic notation for trace prefixes. For t 2 M ( Sigma; D) a 2 Sigma and A Sigma let a (t) uf u t j jtj a = juj a g and A (t) F a2A a (t) In particular ; t) 1 and Sigma (t) max(t) t: Thus, a (t) resp. A (t) ....

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....and on the regular languages we consider, in order to be able to compute R (L) In this paper we consider permutation rewriting rules of the form ab ba, where a; b are letters of a given alphabet Sigma. Such rewriting rules are usually called semi commutation rules in Mazurkiewicz trace theory [7]. Our primary goal is to determine a suitable subclass of regular languages for which we can effectively compute the R closure, for any semi commutation rewriting system R. The problem of computing the closure of a language under a semi commutation rewriting systems appears naturally in several ....

....sets. For example, Pi 1 is precisely the class SRE [1] for which it can be shown that inclusion can be checked in polynomial time. Related work: Problems related to closure of languages under semi commutations have been studied in the community of trace theory (see e.g. chapter 12 in [7] for a survey) However, the problems addressed here and our results have a different flavor. Our aim is to identify subclasses of regular languages which are closed under all semicommutation rewriting relations, whereas classical results of trace theory aim at providing for a given ....

[Article contains additional citation context not shown here]

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

.... logic of linear time (LTL) 15, 10] temporal logic of branching time (BTL) 7] and partial order temporal logic [21] Mazurkiewicz traces and trace systems [13] are partial order structures frequently used to give semantics to concurrent programs and interpreting propositional temporal logics ([12, 6], ISTL [11] TrPTL [26] TSL [22] TLC [1] The first order versions of temporal logics are intended for specifying and proving properties of infinite state concurrent programs [23] The process of program verification requires either a relatively complete program proof rules or a complete proof ....

....of the Concurrent Factorial program is given in Section 6. Section 8 contains some general remarks. 2 Trace Transition Systems The trace systems were introduced by Mazurkiewicz [13] as semantics of Elementary Net Systems. The trace systems are isomorphic to the trace transition systems [22, 6], which form a subclass of the occurrence transition systems [17, 6] The trace transition systems enjoy a nice structural characterization, which is taken as their definition here. The concept of a trace transition system captures the main features of the transition relation w a w 0 from a ....

[Article contains additional citation context not shown here]

V. Diekert and G. Rozenberg, editors. Book of Traces. World Scientific, Singapore. 1995.

....all events of P , for every process P . In general, the visual order provides more ordering than intended by the designer. Therefore we associate with every chart a causal structure providing the intended ordering. Causal structures are related to pomsets [11] event structures [9] and traces [5]. A causal structure is obtained from an MSC by means of a given semantics. Formally, the causal structure of an MSC M is a quintuple tr(M ) hE; OE; L; T; Pi, where the only component that differs from the definition of an MSC is the relation OE, called the precedence order of events. For two ....

....considering a message pair as a single letter we obtain an isomorphism between the causal orders of a natural subclass of message sequence charts and partial orders of semitraces. Semi traces are objects known from the algebraic study of concurrency (for a survey on semi traces see Chapter 12 in [5]) Formally, assume that P = fP 1 ; Pmg is the set of processes. We associate an alphabet Sigma = fm ij j 1 i 6= j mg and a non commutation relation SD Sigma Theta Sigma , SD = f(m ij ; m ik ) j j 6= i 6= kg[f(m ij ; m jk ) j i 6= j 6= kg. The idea underlying SD is to consider in ....

[Article contains additional citation context not shown here]

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

No context found.

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....than in the case of trace monoids, and when applying our method in this special case we still obtain a better complexity result as known previously. 2 Preliminaries 2. 1 Free partially commutative monoids with involution Let us recall some basic concepts of trace theory, for details we refer to [6]. By Gamma we mean a finite alphabet which is equipped with an involution : Gamma Gamma . An involution is a mapping such that a = a for all a 2 Gamma . By I Gamma Theta Gamma we denote an independence relation, its complement is D = Gamma Theta Gamma )nI. It is called a dependence ....

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....of causally independent actions that can be naturally grouped together into equivalence classes where two computations are equated in case they are two di#erent interleavings of the same partially ordered stretch of behavior. This observation led to the notion of Mazurkiewicz traces [DM97, DR95] Traces can be understood as partially commutative words that model the behavior of a concurrent system. While the study of partially commutative monoids traces back to implementation. For example, we also call a protocol definition in some formal language an implementation rather than only its ....

....of) words allows the employment of the rich theory of (finite) automata. In this section, we bring out the concept of linearizations providing a link between traces and (certain) equivalence classes of words. We limit our examination to the extent that is needed for our later developments. Confer [DR95] for a thorough investigation on their relationship. As usual, a word w over # is a sequence of elements of #. It is called finite respectively infinite if the sequence is finite respectively infinite. The empty word is written as #. The length of a finite word w = a 0 . a n 1 is n and ....

[Article contains additional citation context not shown here]

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....for example that the universality problem for this class is EXPSPACE complete. The same complexity bound follows for both MSC problems. Furthermore, we show that the connectivity property for automata is co NP complete. 2 Preliminaries We first recall the notion of Mazurkiewicz (semi ) traces, [6, 10]. An independence alphabet is a pair (A; I) where A is an alphabet endowed by an irreflexive relation I A Theta A, called independence relation (or commutation relation) Note that we do not assume that I is symmetric. With a given independence alphabet (A; I) we associate a rewriting relation ....

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

....investigated in this paper but they will be the subject of a forthcoming paper. Also, we do not consider the shuffle operation between trace languages, introduced in [32] although trace languages are widely investigated in connection to parallel computation and the theory of concurrency, see [1] [7], 8] 33] The syntactic constraints that we consider here are based on the notion of a trajectory. Roughly speaking, a trajectory is a segment of a line in plane, starting in the origin of axes and continuing parallel with the axis Ox or Oy. The line can change its direction only in points of ....

V. Diekert and G. Rozenberg (ed.), The Book of Traces, World Scientific, Singapore, 1995.

No context found.

V. Diekert and G. Rozenberg (Eds.) The Book of Traces. World Scientific, 1995.

No context found.

V. Diekert and G. Rozenberg (Eds.) The Book of Traces. World Scientific, 1995.

No context found.

V. Diekert and G. Rozenberg (Eds.). The Book of Traces. World Scientific, 1995.

No context found.

V. Diekert and G. Rozenberg, editors. Book of Traces. World Scientific, Singapore. 1995.

No context found.

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, 1995.

No context found.

Diekert, V., Rozenberg, G. (Eds.): The Book of Traces. World Scientific (1995)

No context found.

V. Diekert and G. Rozenberg, editors. Book of Traces. World Scientific, Singapore, 1995.

No context found.

V. Diekert and G. Rozenberg, editors. The Book of Traces. World Scientific, Singapore, 1995.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC