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Two optimal parallel algorithms on the commutation class of a word

Identifieur interne : 000626 ( PascalFrancis/Corpus ); précédent : 000625; suivant : 000627

Two optimal parallel algorithms on the commutation class of a word

Auteurs : René Schott ; Jean-Claude Spehner

Source :

RBID : Pascal:04-0519357

Descripteurs français

English descriptors

Abstract

The free partially commutative monoid M(A, Θ) defined by a set of commutation relations Θ on an alphabet A can be viewed as a model for concurrent computing: indeed, the independence or the simultaneity of two actions can be interpreted by the commutation of two letters that encode them. In this context, the commutation class CΘ(w) of a word w of the free monoid A* plays a crucial role. The main results presented in this paper are the following: - A characterization of the minimal automaton AΘ(w) for CΘ(w) with the help of the new notion of Θ-dissection. - A parallel algorithm which computes the minimal automaton AΘ(w). This algorithm is optimal if the size of A is constant. - An optimal parallel algorithm for testing if a word belongs to the commutation class CΘ (w). Our approach differs completely from the methods (based on Foata's normal form) used by Cérin and Petit (Application de la théorie des traces à l'implantation et à la mesure d'algorithmes de distribution, Thèse Université Paris 11, Centre d'Orsay, 1993; Proc. 6th Intemat. Parallel Processing Symp. (IPPS), IEEE Press, New York, 1992, pp. 374-379; Proc. MFCS'93, Lecture Notes in Computer Science, Vol. 711, Springer, Berlin, 1993, pp. 332-341) for solving similar problems. Under some assumptions the first algorithm achieves an optimal speedup. The second algorithm achieves also an optimal speedup and has a time complexity in O(log n) if the number of processors is in O(n) where n is the length of the word w, the total number of operations is in O(n) and does not depend on the size of the alphabet A as for the classical sequential algorithm.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A08 01  1  ENG  @1 Two optimal parallel algorithms on the commutation class of a word
A09 01  1  ENG  @1 Words, languages and combinatorics: 3rd International Colloquium, Kyoto, Japan, March 14-18, 2000 (selected and revised papers)
A11 01  1    @1 SCHOTT (René)
A11 02  1    @1 SPEHNER (Jean-Claude)
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Format Inist (serveur)

NO : PASCAL 04-0519357 INIST
ET : Two optimal parallel algorithms on the commutation class of a word
AU : SCHOTT (René); SPEHNER (Jean-Claude); ITO (Masami)
AF : LORIA and IECN, Universiré Henri Poincaré/54506 Vandoeuvre-lès-Nancy/France (1 aut.); Laboratoire MAGE, Faculté des Sciences et Techniques, Université de Haute Alsace/68093, Mulhouse/France (2 aut.); Faculty of Science, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-ku/Kyoto 603/Japon (1 aut.)
DT : Publication en série; Congrès; Niveau analytique
SO : Theoretical computer science; ISSN 0304-3975; Coden TCSCDI; Pays-Bas; Da. 2004; Vol. 324; No. 1; Pp. 107-131; Bibl. 13 ref.
LA : Anglais
EA : The free partially commutative monoid M(A, Θ) defined by a set of commutation relations Θ on an alphabet A can be viewed as a model for concurrent computing: indeed, the independence or the simultaneity of two actions can be interpreted by the commutation of two letters that encode them. In this context, the commutation class CΘ(w) of a word w of the free monoid A* plays a crucial role. The main results presented in this paper are the following: - A characterization of the minimal automaton AΘ(w) for CΘ(w) with the help of the new notion of Θ-dissection. - A parallel algorithm which computes the minimal automaton AΘ(w). This algorithm is optimal if the size of A is constant. - An optimal parallel algorithm for testing if a word belongs to the commutation class CΘ (w). Our approach differs completely from the methods (based on Foata's normal form) used by Cérin and Petit (Application de la théorie des traces à l'implantation et à la mesure d'algorithmes de distribution, Thèse Université Paris 11, Centre d'Orsay, 1993; Proc. 6th Intemat. Parallel Processing Symp. (IPPS), IEEE Press, New York, 1992, pp. 374-379; Proc. MFCS'93, Lecture Notes in Computer Science, Vol. 711, Springer, Berlin, 1993, pp. 332-341) for solving similar problems. Under some assumptions the first algorithm achieves an optimal speedup. The second algorithm achieves also an optimal speedup and has a time complexity in O(log n) if the number of processors is in O(n) where n is the length of the word w, the total number of operations is in O(n) and does not depend on the size of the alphabet A as for the classical sequential algorithm.
CC : 001D02A05; 001D02A03
FD : Algorithme optimal; Algorithme parallèle; Monoïde libre; Relation commutation; Calcul automatique; Simultanéité; Lettre alphabet; Forme normale; Automate; Traitement parallèle; Complexité temps; Longueur mot; Méthode séquentielle; Informatique théorique; Automate minimal; Algorithme séquentiel
ED : Optimal algorithm; Parallel algorithm; Free monoid; Commutation relation; Computing; Simultaneity; Letter; Normal form; Automaton; Parallel processing; Time complexity; Word length; Sequential method; Computer theory
SD : Algoritmo óptimo; Algoritmo paralelo; Monoide libre; Relación conmutación; Cálculo automático; Simultaneidad; Letra alfabeto; Forma normal; Autómata; Tratamiento paralelo; Complejidad tiempo; Longitud palabra; Método secuencial; Informática teórica
LO : INIST-17243.354000120225890060
ID : 04-0519357

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<s0>Simultaneity</s0>
<s5>26</s5>
</fC03>
<fC03 i1="06" i2="X" l="SPA">
<s0>Simultaneidad</s0>
<s5>26</s5>
</fC03>
<fC03 i1="07" i2="X" l="FRE">
<s0>Lettre alphabet</s0>
<s5>27</s5>
</fC03>
<fC03 i1="07" i2="X" l="ENG">
<s0>Letter</s0>
<s5>27</s5>
</fC03>
<fC03 i1="07" i2="X" l="SPA">
<s0>Letra alfabeto</s0>
<s5>27</s5>
</fC03>
<fC03 i1="08" i2="X" l="FRE">
<s0>Forme normale</s0>
<s5>29</s5>
</fC03>
<fC03 i1="08" i2="X" l="ENG">
<s0>Normal form</s0>
<s5>29</s5>
</fC03>
<fC03 i1="08" i2="X" l="SPA">
<s0>Forma normal</s0>
<s5>29</s5>
</fC03>
<fC03 i1="09" i2="X" l="FRE">
<s0>Automate</s0>
<s5>35</s5>
</fC03>
<fC03 i1="09" i2="X" l="ENG">
<s0>Automaton</s0>
<s5>35</s5>
</fC03>
<fC03 i1="09" i2="X" l="SPA">
<s0>Autómata</s0>
<s5>35</s5>
</fC03>
<fC03 i1="10" i2="X" l="FRE">
<s0>Traitement parallèle</s0>
<s5>36</s5>
</fC03>
<fC03 i1="10" i2="X" l="ENG">
<s0>Parallel processing</s0>
<s5>36</s5>
</fC03>
<fC03 i1="10" i2="X" l="SPA">
<s0>Tratamiento paralelo</s0>
<s5>36</s5>
</fC03>
<fC03 i1="11" i2="X" l="FRE">
<s0>Complexité temps</s0>
<s5>41</s5>
</fC03>
<fC03 i1="11" i2="X" l="ENG">
<s0>Time complexity</s0>
<s5>41</s5>
</fC03>
<fC03 i1="11" i2="X" l="SPA">
<s0>Complejidad tiempo</s0>
<s5>41</s5>
</fC03>
<fC03 i1="12" i2="X" l="FRE">
<s0>Longueur mot</s0>
<s5>43</s5>
</fC03>
<fC03 i1="12" i2="X" l="ENG">
<s0>Word length</s0>
<s5>43</s5>
</fC03>
<fC03 i1="12" i2="X" l="SPA">
<s0>Longitud palabra</s0>
<s5>43</s5>
</fC03>
<fC03 i1="13" i2="X" l="FRE">
<s0>Méthode séquentielle</s0>
<s5>44</s5>
</fC03>
<fC03 i1="13" i2="X" l="ENG">
<s0>Sequential method</s0>
<s5>44</s5>
</fC03>
<fC03 i1="13" i2="X" l="SPA">
<s0>Método secuencial</s0>
<s5>44</s5>
</fC03>
<fC03 i1="14" i2="X" l="FRE">
<s0>Informatique théorique</s0>
<s5>45</s5>
</fC03>
<fC03 i1="14" i2="X" l="ENG">
<s0>Computer theory</s0>
<s5>45</s5>
</fC03>
<fC03 i1="14" i2="X" l="SPA">
<s0>Informática teórica</s0>
<s5>45</s5>
</fC03>
<fC03 i1="15" i2="X" l="FRE">
<s0>Automate minimal</s0>
<s4>INC</s4>
<s5>70</s5>
</fC03>
<fC03 i1="16" i2="X" l="FRE">
<s0>Algorithme séquentiel</s0>
<s4>INC</s4>
<s5>71</s5>
</fC03>
<fN21>
<s1>292</s1>
</fN21>
<fN44 i1="01">
<s1>OTO</s1>
</fN44>
<fN82>
<s1>OTO</s1>
</fN82>
</pA>
<pR>
<fA30 i1="01" i2="1" l="ENG">
<s1>International Colloquium on Words, Languages and Combinaritics</s1>
<s2>3</s2>
<s3>Kyoto JPN</s3>
<s4>2000-03-14</s4>
</fA30>
</pR>
</standard>
<server>
<NO>PASCAL 04-0519357 INIST</NO>
<ET>Two optimal parallel algorithms on the commutation class of a word</ET>
<AU>SCHOTT (René); SPEHNER (Jean-Claude); ITO (Masami)</AU>
<AF>LORIA and IECN, Universiré Henri Poincaré/54506 Vandoeuvre-lès-Nancy/France (1 aut.); Laboratoire MAGE, Faculté des Sciences et Techniques, Université de Haute Alsace/68093, Mulhouse/France (2 aut.); Faculty of Science, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-ku/Kyoto 603/Japon (1 aut.)</AF>
<DT>Publication en série; Congrès; Niveau analytique</DT>
<SO>Theoretical computer science; ISSN 0304-3975; Coden TCSCDI; Pays-Bas; Da. 2004; Vol. 324; No. 1; Pp. 107-131; Bibl. 13 ref.</SO>
<LA>Anglais</LA>
<EA>The free partially commutative monoid M(A, Θ) defined by a set of commutation relations Θ on an alphabet A can be viewed as a model for concurrent computing: indeed, the independence or the simultaneity of two actions can be interpreted by the commutation of two letters that encode them. In this context, the commutation class C
<sub>Θ</sub>
(w) of a word w of the free monoid A* plays a crucial role. The main results presented in this paper are the following: - A characterization of the minimal automaton A
<sub>Θ</sub>
(w) for C
<sub>Θ</sub>
(w) with the help of the new notion of Θ-dissection. - A parallel algorithm which computes the minimal automaton A
<sub>Θ</sub>
(w). This algorithm is optimal if the size of A is constant. - An optimal parallel algorithm for testing if a word belongs to the commutation class C
<sub>Θ </sub>
(w). Our approach differs completely from the methods (based on Foata's normal form) used by Cérin and Petit (Application de la théorie des traces à l'implantation et à la mesure d'algorithmes de distribution, Thèse Université Paris 11, Centre d'Orsay, 1993; Proc. 6th Intemat. Parallel Processing Symp. (IPPS), IEEE Press, New York, 1992, pp. 374-379; Proc. MFCS'93, Lecture Notes in Computer Science, Vol. 711, Springer, Berlin, 1993, pp. 332-341) for solving similar problems. Under some assumptions the first algorithm achieves an optimal speedup. The second algorithm achieves also an optimal speedup and has a time complexity in O(log n) if the number of processors is in O(n) where n is the length of the word w, the total number of operations is in O(n) and does not depend on the size of the alphabet A as for the classical sequential algorithm.</EA>
<CC>001D02A05; 001D02A03</CC>
<FD>Algorithme optimal; Algorithme parallèle; Monoïde libre; Relation commutation; Calcul automatique; Simultanéité; Lettre alphabet; Forme normale; Automate; Traitement parallèle; Complexité temps; Longueur mot; Méthode séquentielle; Informatique théorique; Automate minimal; Algorithme séquentiel</FD>
<ED>Optimal algorithm; Parallel algorithm; Free monoid; Commutation relation; Computing; Simultaneity; Letter; Normal form; Automaton; Parallel processing; Time complexity; Word length; Sequential method; Computer theory</ED>
<SD>Algoritmo óptimo; Algoritmo paralelo; Monoide libre; Relación conmutación; Cálculo automático; Simultaneidad; Letra alfabeto; Forma normal; Autómata; Tratamiento paralelo; Complejidad tiempo; Longitud palabra; Método secuencial; Informática teórica</SD>
<LO>INIST-17243.354000120225890060</LO>
<ID>04-0519357</ID>
</server>
</inist>
</record>

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