Abstract
The concept of traces has been introduced for describing non-sequential behaviour of concurrent systems via its sequential observations. Traces represent concurrent processes in the same way as strings represent sequential ones. The theory of traces can be used as a tool for reasoning about nets and it is hoped that applying this theory one can get a calculus of the concurrent processes analogous to that available for sequential systems. The following topics will be discussed: algebraic properties of traces, trace models of some concurrency phenomena, fixed-point calculus for finding the behaviour of nets, modularity, and some applications of the presented theory.
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7. References
AALBERSBERG IJ. J., ROZENBERG, G.: "Traces, dependency graphs and DNLC grammars”, Discrete Applied Mathematics 11 (1985) 299–306
AALBERSBERG, IJ. J., ROZENBERG, G.: "Trace languages defined by context-free languages", manuscript, (1985)
AALBERSBERG, IJ. J., WELZL, E.: "Trace languages defined by regular string languages", to appear (1985)
BERTONI, A., BRAMBILLA, M., MAURI, G., SABADINI, N.: "An application of the theory of free partially commutative monoids: asymptotic densities of trace languages", Lecture Notes in Computer Science 118 (1981) 205–215
BERTONI, A. and GOLDWURM, M.: "Average analysis of an algorithm for a membership problem of trace languages", manuscript, (1986)
BERTONI, A., MAURI, G., SABADINI, N.: "A hierarchy of regular trace languages and some combinatorial applications", Proc. 2nd World Conf. on Math. at the Serv. of Men, Las Palmas (1982) 146–153
BERTONI, A., MAURI, G., SABADINI, N.: "Equivalence and membership problems for regular trace languages", Lecture Notes in Computer Science 140 (1982) 61–71
BERTONI, A., MAURI, G., SABADINI, N.: "Context — free trace languages", Proc. 7th CAAP, Lille (1982) 32–42
BERTONI, A., MAURI, G., SABADINI, N.: "Equivalence and membership problems for regular and context — free trace languages", manuscript (1982)
BERTONI, A., MAURI, G., SABADINI, N.: "Concurrency and commutativity", manuscript (1982)
BERTONI, A., MAURI, G., SABADINI, N.: "Unambiguous regular trace languages", Proc. Colloq. on Algebra, Combinat. and Comp. Science, Gyor (1983)
BERTONI, A., MAURI, G., SABADINI, N.: "Representation of prefixes of a trace and membership problem for context — free trace languages", manuscript (1985)
BEST, E., FERNANDEZ, C. and PLUNNECKE, H.: "Concurrent systems and processes", manuscript (1985)
CARPI, A. and LUCA, A. de: "Square — free words on partially commutative free monoids", Information Processing Letters 22 (1986) 125–132
CARTIER, P. and FOATA, D.: "Problemes combinatoires de commutation et rearrangements", Lecture Notes in Mathematics 85 (1969)
CLERBOUT, M. and LATTEUX, M.: "Partial commutations and faithful rational transductions", Theoretical Computer Science 34 (1984) 241–254
CLERBOUT, M. and LATTEUX, M.: "Semi — commutations", Techn. Rep. IT-63-84, Equipe Lilloise d'Inform. Theor., Univers. de Lille 1, Villeneuve d'Ascq. (1984)
CORI, R. and METIVIER, Y.: "Recognizable subsets of some partially abelian monoids", Theoretical Computer Science 35 (1984) 179–189
CORI, R. and PERRIN, D.: "Automates and commutations partielles", RAIRO Informatique Theorique 19 (1985) 21–32
DUBOC, C.: "Some properties of commutation in free partially commutative monoids", Information Processing Letters 20 (1985) 1–4
DUBOC, C.: "Equations in free partially commutative monoids", Lecture Notes in Computer Science 210 (1986) 192–202
EHRENFEUCHT, A., ROZENBERG, G.: "On the Structure of Dependence Graphs", Rapport 87-02, Dept. of Computer Science, University of Leiden (1987)
FLE, M. P. and ROUCAIROL, G.: "On serializability of iterated transactions", Proc. ACM SIGACT-SIGOPS Symp. on Princ. of Distrib. Comp., Ottawa (1982) 194–200
FLE, M. P. and ROUCAIROL, G.: "Fair serializability of iterated transactions using FIFO — nets", Lecture Notes in Computer Science 188 (1985) 154–168
FLE, M. P. and ROUCAIROL, G.: "Maximal serializability of iterated transactions", Theoretical Computer Science 38 (1985) 1–16
FOATA, D.: "Rearrangements of words", in M. Lothaire: Combinatorics on words, Addison-Wesley, Reading, (1983) Chapter 10
GRABOWSKI, J.: "On partial languages", Fundamenta Informaticae 4 (1981) 427–498
GYORY, G., KNUTH, E., RONYAI, L.: "Grammatical projections 1. Elementary constructions", Working Paper II/3, MTA SZTAKI, Budapest (1979)
JANICKI, R.: "Synthesis of concurrent schemes", Lecture Notes in Computer Science 64 (1978) 298–307
JANICKI, R.: "On the design of concurrent systems", Proc. 2nd Intern. Conf. on Distrib. Comp. Systems, Paris (1981) 455–466
JANICKI, R.: "Mazurkiewicz traces semantics for communicating sequential processes", Proc. 5th European Workshop on Appl. and Theory of Petri Nets, Aarhus (1984) 50–70
JANICKI, R.: "Trace semantics for communicating sequential processes", Techn. Rep. R-85-12, Inst. for Elektr. Syst., Alaborg Univ., Aalborg (1985)
KELLER, R. M.: "A solvable program-schema equivalence problem", Proc. 5th Ann. Princeton Conf. on Inf. Sciences and Systems, Princeton (1971) 301–306
KNUTH, E.: "Petri nets and regular trace languages", manuscript (1978)
KNUTH, E.: "Petri nets and trace languages", Proc. 1st Europ. Conf. on Parallel and Distr. Processing, Toulouse (1979) 51–56
KNUTH, E. and GYORY, G.: "Paths and traces", Computational Linguistics and Computer Languages 13 (1979) 31–42
LAUER, P.E., SHIELDS, M.W., BEST, E.: "Formal Theory of the Basic COSY Notation", Technical Report 143, Computing Laboratory, University of Newcastle upon Tyne (1979)
LEVI F. W.: "On semigroups", Bull. of the Calcutta Math. Soc. 36 (1944) 141–146
MAZURKIEWICZ, A.: "Concurrent program schemes and their interpretations", DAIMI Rep. PB-78, Aarhus Univ., Aarhus (1977)
MAZURKIEWICZ, A.: "Equational semantics of concurrent systems", Proc. 8th Spring School on Comp. Sci., Colleville sur mer (1980)
MAZURKIEWICZ, A.: "A calculus of execution traces for concurrent systems", manuscript (1983)
MAZURKIEWICZ, A.: "Traces, histories, graphs: instances of a process monoid", Lecture Notes in Computer Science 176 (1984) 115–133
MAZURKIEWICZ, A.: "Semantics of concurrent systems: a modular fixed-point trace approach", Lecture Notes in Computer Science 188 (1985) 353–375
MAZURKIEWICZ, A.: "Trace Theory", Advances in Petri Nets 1986, Part II, Proceedings of an Advanced Course Lecture Notes in Computer Science 255 (1987) 279–324
METIVIER, Y.: "Une condition suffisante de reconaissabilite dans un monoide partiellement commutatif", Techn. Rep. 8417, U.E.R. de Math. et d'Inform., Univ. de Bordeaux, Bordeaux (1984)
METIVIER, Y.: "Sous-ensemble reconnaisable d'un monoide partiellment commutatif libre", manuscript (1985)
NIELSEN, M., PLOTKIN, G., WINSKEL, G.: "Petri nets, event structures and domains, Part 1", Theoretical Computer Science 13 (1981) 85–108
OCHMANSKI, E.: "Regular trace languages", Ph. D. Thesis (1985) (summary in Bull. of EATCS 27, 1985)
Perrin, D.: "Words over a partially commutative alphabet", NATO ASI Series F12 (1985) 329–340
PETRI, C.A.: "Concepts of Net Theory", Proceedings of the Symposium and Summer School on MFCS'73, High Tatras (1973)
PETRI, C.A.: "Non-Sequential Processes", GMD-ISF Report 77.05, Gesellschaft fuer Mathematik und Datenverarbeitung mbH Bonn (1977)
REISIG, W.: "Petri nets — an introduction", EATCS Monographs on Theoretical Computer Science, Springer Verlag (1985)
REM, M.: "Concurrent Computations and VLSI Circuits", Control Flow and Data Flow: Concepts of Distributed Programming (M. Broy, editor), Springer (1985) 399–437
ROZENBERG, G.: "Behaviour of elementary net systems", Advances in Petri Nets 1986, Part I, Proceedings of an Advanced Course Lecture Notes in Computer Science 254 (1987) 60–94
ROZENBERG, G., THIAGARAJAN, P.S.: "Petri Nets: Basic Notions, Structure and Behaviour", Lecture Notes in Computer Science 224, (1986) 585–668
RYTTER, W.: "Some properties of trace languages", Fundamenta Informaticae 7 (1984) 117–127
SAKAROVITCH, J.: "On regular trace languages", to appear (1986)
SHIELDS, M.W.: "Adequate Path Expressions", Lecture Notes in Computer Science 70, (1979) 249–265
SHIELDS, M.W.: "Non-Sequential Behaviour", Part 1, Int. Report CSR-120-82, Dept. of Computer Science, University of Edinburgh (1982)
SHIELDS, M.W.: "Concurrent Machines", The Computer Journal 28, Nr. 5 (1988) 449–466
STARKE, P. H.: "Processes in Petri Nets", Elektron. Inf. und Kyb. 17 (1981)
STARKE, P. H.: "Traces and semiwords", Lecture Notes in Computer Science 208 (1985) 332–349
SZIJARTO, M.: "A classification and closure properties of languages for describing concurrent system behaviours", Fundamenta Informaticae 4 (1981) 531–549
TARLECKI, A.: "Notes on the implementability of formal languages by concurrent systems", ICS PAS Report 481, Inst. of Comp. Science, Polish Academy of Sciences, Warszawa (1982)
THIAGARAJAN, P.S.: "Elementary net systems", Advances in Petri Nets 1986, Part I, Proceedings of an Advanced Course Lecture Notes in Computer Science 254 (1987) 26–59
ZIELONKA, W.: "Proving assertions about parallel programs by means of traces", ICS PAS Report 424, Inst. of Comp. Science, Polish Academy of Sciences, Warszawa (1980)
ZIELONKA, W.: "The notes on finite state asynchronous automata and trace languages", manuscript (1982)
ZIELONKA, W.: "Notes on Finite Asynchronous Automata", Informatique Theorique et Applications 21, Nr. 2, (1987) 99–135
ZUIDWEG, H.: "Trace approach to synchronic distances" (manuscript), University of Leiden, Leiden (1986)
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Mazurkiewicz, A. (1989). Basic notions of trace theory. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds) Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. REX 1988. Lecture Notes in Computer Science, vol 354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013025
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DOI: https://doi.org/10.1007/BFb0013025
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