Linear process algebra
Pages 92 - 111
Abstract
A linear process is a system of events and states related by an inner product, on which are defined the behaviorally motivated operations of tensor product or orthocurrence, sum or concurrence, sequence, and choice. Linear process algebra or LPA is the theory of this framework. LPA resembles Girard's linear logic with the differences attributable to its focus on behavior instead of proof. As with MLL the multiplicative part can be construed via the Curry-Howard isomorphism as an enrichment of Boolean algebra. The additives cater for independent concurrency or parallel play. The traditional sequential operations of sequence and choice exploit process-specific state information catering for notions of transition and cancellation.
References
[1]
Allen, J.F.: Towards a general theory of action and time. Artificial Intelligence 23, 123-154 (1984).
[2]
Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge University Press, Cambridge (1990).
[3]
Barr, M.: *-Autonomous categories. Lecture Notes in Mathematics, vol. 752. Springer, Heidelberg (1979).
[4]
Barr, M.: *-Autonomous categories and linear logic. Math Structures in Comp. Sci. 1(2), 159-178 (1991).
[5]
Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Information and Control 60, 109-137 (1984).
[6]
Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.): Handbook of Process Algebra. Elsevier (North-Holland), Amsterdam (2000).
[7]
Brookes, S.D., Hoare, C.A.R., Roscoe, A.D.: A theory of communicating sequential processes. Journal of the ACM 31(3), 560-599 (1984).
[8]
Brown, C., Gurr, D.: A categorical linear framework for Petri nets. In: Mitchell, J. (ed.) Logic in Computer Science, pp. 208-218. IEEE Computer Society, Los Alamitos (June 1990).
[9]
Brown, C., Gurr, D., de Paiva, V.: A linear specification language for Petri nets. Technical Report DAIMI PB-363, Computer Science Department, Aarhus University (October 1991).
[10]
Buckland, R., Johnson, M.: Echidna: A system for manipulating explicit choice higher dimensional automata. In: Nivat, M., Wirsing, M. (eds.) AMAST 1996. LNCS, vol. 1101, Springer, Heidelberg (1996).
[11]
Casley, R.T., Crew, R.F., Meseguer, J., Pratt, V.R.: Temporal structures. Math. Structures in Comp. Sci. 1(2), 179-213 (1991).
[12]
Fajstrup, L., Goubault, E., Raussen, M.: Detecting deadlocks in concurrent systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 332-347. Springer, Heidelberg (1998).
[13]
Gabriel, P., Ulmer, F.: Lokal präsentierbare Kategorien. Lecture Notes in Mathematics, vol. 221. Springer, Heidelberg (1971).
[14]
Gaifman, H., Pratt, V.R.: Partial order models of concurrency and the computation of functions. In: Proc. 2nd Annual IEEE Symp. on Logic in Computer Science, Ithaca, NY, pp. 72-85 (June 1987).
[15]
Ginsburg, S., Spanier, E.H.: Mappings of languages by two-tape devices. Journal of the ACM 12, 423-434 (1965).
[16]
Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1-102 (1987).
[17]
Gischer, J.L.: The equational theory of pomsets. Theoretical Computer Science 61, 199-224 (1988).
[18]
van Glabbeek, R.J., Vaandrager, F.W.: Petri net models for algebraic theories of concurrency. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259, pp. 224-242. Springer, Heidelberg (1987).
[19]
Goubault, E.: Homology of higher-dimensional automata. In: CONCUR 1993. LNCS, vol. 630, pp. 254-268. Springer, Heidelberg (1993).
[20]
Goubault, E.: The Geometry of Concurrency. PhD thesis, École Normale Supérieure (1995).
[21]
Goubault, E.: Schedulers as abstract interpretations of hda. In: Proc. of PEPM 1995, La Jolla, ACM Press, New York (June 1995).
[22]
Goubault, E.: Durations for truly-concurrent actions. In: Riis Nielson, H. (ed.) ESOP 1996. LNCS, vol. 1058, pp. 173-187. Springer, Heidelberg (1996).
[23]
Goubault, E.: A semantic view on distributed computability and complexity. In: Proceedings of the 3rd Theory and Formal Methods Section Workshop, Imperial College Press, London (1996).
[24]
Goubault, E.: Geometry and concurrency. Mathematical Structures in Computer Science, Special Issue 10(4), 409-573 (7 papers) (2000).
[25]
Goubault, E., Cridlig, R.: Semantics and analysis of Linda-based languages. In: Cousot, P., Filé, G., Falaschi, M., Rauzy, A. (eds.) WSA 1993. LNCS, vol. 724, pp. 72-86. Springer, Heidelberg (1993).
[26]
Goubault, E., Jensen, T.P.: Homology of higher dimensional automata. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 254-268. Springer, Heidelberg (1992).
[27]
Grabowski, J.: On partial languages. Fundamenta Informaticae IV(2), 427-498 (1981).
[28]
Greif, I.: Semantics of Communicating Parallel Processes. PhD thesis, Project MAC report TR-154, MIT (1975).
[29]
Gunawardena, J.: Homotopy and concurrency. EATCS Bulletin 54, 184-193 (1994).
[30]
Gupta, V.: Chu Spaces: A Model of Concurrency. PhD thesis, Stanford University, Tech. Report (September 1994), http://boole.stanford.edu/pub/gupthes.pdf.
[31]
Gupta, V., Pratt, V.R.: Gates accept concurrent behavior. In: Proc. 34th Ann. IEEE Symp. on Foundations of Comp. Sci., pp. 62-71 (November 1993).
[32]
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Boston (2000).
[33]
Hoare, C.A.R.: Communicating sequential processes. Communications of the ACM 21(8), 666-672 (1978).
[34]
Lafont, Y.: The linear abstract machine. TCS 59, 157-180 (1988).
[35]
Lafont, Y., Streicher, T.: Games semantics for linear logic. In: Proc. 6th Annual IEEE Symp. on Logic in Computer Science, Amsterdam, pp. 43-49 (July 1991).
[36]
Lambek, J., Scott, P.: Introduction to Higher-Order Categorical Logic. Cambridge University Press, Cambridge (1986).
[37]
Mazurkiewicz, A.: Concurrent program schemes and their interpretations. Technical Report DAIMI Report PB-78, Aarhus University, Aarhus (1977).
[38]
Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980).
[39]
Nielsen, M., Plotkin, G., Winskel, G.: Petri nets, event structures, and domains, part I. Theoretical Computer Science 13, 85-108 (1981).
[40]
Papadimitriou, C.: The Theory of Database Concurrency Control. Computer Science Press, Rockville (1986).
[41]
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167-183. Springer, Heidelberg (1981).
[42]
Petri, C.A.: Fundamentals of a theory of asynchronous information flow. In: Proc. IFIP Congress 62, Munich, pp. 386-390. North-Holland, Amsterdam (1962).
[43]
Plotkin, G.D.: Lambda definability in the full type hierarchy. In: To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp. 363-373. Academic Press, London (1980).
[44]
Plotkin, G.D.: A structural approach to operational semantics. Technical Report Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark (1981); Reprinted with corrections in J. Log. Algebr. Program. (60-61), 17-139 (2004).
[45]
Pnueli, A.: The temporal logic of programs. In: 18th IEEE Symposium on Foundations of Computer Science, pp. 46-57 (October 1977).
[46]
Pratt, V.R.: Semantical considerations on Floyd-Hoare logic. In: Proc. 17th Ann. IEEE Symp. on Foundations of Comp. Sci., pp. 109-121 (October 1976).
[47]
Pratt, V.R.: Process logic. In: Proc. 6th Ann. ACM Symposium on Principles of Programming Languages, San Antonio, pp. 93-100 (January 1979).
[48]
Pratt, V.R.: On the composition of processes. In: Proceedings of the Ninth Annual ACM Symposium on Principles of Programming Languages (January 1982).
[49]
Pratt, V.R.: Position statement. Circulated at the Panel on Mathematics of Parallel Processes, chair A.R.G. Milner, IFIP-83 (September 1983).
[50]
Pratt, V.R.: The pomset model of parallel processes: Unifying the temporal and the spatial. In: Seminar on Concurrency. LNCS, vol. 197, pp. 180-196. Springer, Heidelberg (1984).
[51]
Pratt, V.R.: Some constructions for order-theoretic models of concurrency. In: Logics of Programs. LNCS, vol. 193, pp. 269-283. Springer, Heidelberg (1985).
[52]
Pratt, V.R.: Two-way channel with disconnect. In: The Analysis of Concurrent Systems: Proceedings of a Tutorial and Workshop. LNCS, vol. 207, pp. 110-111. Springer, Heidelberg (1985).
[53]
Pratt, V.R.: Modeling concurrency with partial orders. Int. J. of Parallel Programming 15(1), 33-71 (1986).
[54]
Pratt, V.R.: Modeling concurrency with geometry. In: Proc. 18th Ann. ACM Symposium on Principles of Programming Languages, pp. 311-322 (January 1991).
[55]
Pratt, V.R.: Arithmetic + logic + geometry=concurrency. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 430-447. Springer, Heidelberg (1992).
[56]
Pratt, V.R.: The duality of time and information. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 237-253. Springer, Heidelberg (1992).
[57]
Pratt, V.R.: Event spaces and their linear logic. In: Algebraic Methodology and Software Technology,Workshops in Computing, AMAST 1991, Iowa City, pp. 1-23. Springer, Heidelberg (1992).
[58]
Pratt, V.R.: Chu spaces: complementarity and uncertainty in rational mechanics. Technical report, TEMPUS Summer School, Budapest (July 1994) (manuscript), http://boole.stanford.edu/pub/bud.pdf
[59]
Pratt, V.R.: Time and information in sequential and concurrent computation. In: Ito, T. (ed.) TPPP 1994. LNCS, vol. 907, pp. 1-24. Springer, Heidelberg (1995).
[60]
Pratt, V.R.: Chu spaces and their interpretation as concurrent objects. In: van Leeuwen, J. (ed.) Computer Science Today: Recent Trends and Developments. LNCS, vol. 1000, pp. 392-405. Springer, Heidelberg (1995).
[61]
Pratt, V.R.: Types as processes, via Chu spaces, Santa Margherita. In: Electronic Notes in Theoretical Computer Science, Santa Margherita, vol. 7, p. 21 (1997), http://www.elsevier.nl/locate/entcs/volume7.html
[62]
Pratt, V.R.: Chu spaces: Notes for school on category theory and applications. Technical report, University of Coimbra, Coimbra, Portugal (July 1999) (manuscript) http://boole.stanford.edu/pub/coimbra.pdf
[63]
Pratt, V.R.: Higher dimensional automata revisited. Math. Structures in Comp. Sci. 10, 525-548 (2000).
[64]
Pratt, V.R.: Orthocurrence as both interaction and observation. In: Rodriguez, R., Anger, F. (eds.) Proc. Workshop on Spatial and Temporal Reasoning, IJCAI 2001, Seattle (August 2001).
[65]
Pratt, V.R.: Event-state duality: The enriched case. In: Brim, L., Jančar, P., Křetínsky, M., Kučera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, p. 41. Springer, Heidelberg (2002).
[66]
Pratt, V.R.: Chu spaces as a semantic bridge between linear logic and mathematics. Theoretical Computer Science 294(3), 439-471 (2003); Selected papers from Linear Logic 1996, Tokyo.
[67]
Pratt, V.R.: Transition and cancellation in concurrency and branching time. Math. Structures in Comp. Sci., Special Issue on the Difference Between Sequentiality and Concurrency 13(4), 485-529 (2003).
[68]
Riddle, W.: The Modeling and Analysis of Supervisory Systems. PhD thesis, Computer Science Dept., Stanford University, p. 174 (March 1972).
[69]
Rodriguez, R.V., Anger, F.D.: Branching time via Chu spaces. In: Rodriguez, R., Anger, F. (eds.) Proc. Workshop on Spatial and Temporal Reasoning, IJCAI 2001, Seattle (August 2001).
[70]
Sassone, V., Cattani, G.L.: Higher-dimensional transition systems. In: Proceedings of LICS 1996 (1996).
[71]
Shields, M.: Deterministic asynchronous automata. In: Neuhold, E.J., Chroust, G. (eds.) Formal Models in Programming. Elsevier Science Publishers, B.V., North Holland (1985).
[72]
Takayama, Y.: Extraction of concurrent processes from higher-dimensional automata. In: Kirchner, H. (ed.) CAAP 1996. LNCS, vol. 1059, pp. 72-85. Springer, Heidelberg (1996).
[73]
van Glabbeek, R.: Comparative Concurrency Semantics and Refinement of Actions. PhD thesis, Vrije Universiteit te Amsterdam (May 1990).
[74]
van Glabbeek, R.: Bisimulations for higher dimensional automata (June 1991) (manuscript), http://theory.stanford.edu/~rvg/hda
[75]
van Glabbeek, R.: On the expressiveness of higher dimensional automata. Theoretical Computer Science 356(3), 169-194 (2006).
[76]
Winskel, G.: Events in Computation. PhD thesis, Dept. of Computer Science, University of Edinburgh (1980).
[77]
Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255. Springer, Heidelberg (1987).
[78]
Winskel, G.: An introduction to event structures. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1988. LNCS, vol. 354. Springer, Heidelberg (1989).
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Published: 09 February 2011
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