Abstract
The problem of the cost analysis of concurrent programs can be formulated and studied by dynamic methods based on matrix calculi. However, standard matrix calculi can handle only the case of programs whose dimensions are rigidly fixed. In this paper, the notion of dynamic matrix is presented. Dynamic matrices are special matrices having extensible dimensions (rows and columns) which allow matrix product to be always defined. We put forward the theory of dynamic matrices as the correct framework to study the problems of cost analysis of concurrent programs which can change dynamically their dimensions, i.e. their amount of parallelism.
Work partially supported by ESPRIT BRA Project 6454 CONFER, and by CNR Progetto “Specifica ad alto livello e verifica formale di sistemi digitali” 94.01874.CT7.
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References
Aceto, L., Murphy, D., On the Ill-timed but Well-caused. CONCUR'93, LNCS 715, 97–111, 1993.
Baccelli, F., Cohen, G., Olsder, G., Quadrat, J-P., Synchronization and Linearity, Wiley Series in Probability and Mathematical Statistics, Wiley and Sons, 1992.
Cormen, T., Leiserson, C., Rivest, R., Introduction to Algorithms, MIT-Press, 1989.
Cleaveland, R., Yankelevich, An Operational Framework for Value-Passing POPL'94, 326–338, 1994.
Degano, P. De Nicola, R., Montanari, U., A Distributed Operational Semantics for CCS Based on Condition/Event Systems, Acta Informatica, 26, 59–91, 1988.
Degano, P. De Nicola, R., Montanari, U., Partial Ordering Descriptions and Observations of Nondeterministic Concurrent Processes, LNCS 354, 438–466, 1989.
Elgot, C., Matricial Theory, Journal of Algebra 42, 391–422, 1976.
Ferrari, G., Gorrieri, R., Montanari, U., An Extended Expansion Theorem, TAPSOFT 91, LNCS 494, 29–48, 1991.
van Glabbeek, R., Goltz, U., Equivalence Notions for Concurrent Systems and Refinement of Actions, MFCS'89, LNCS 397, 237–248, 1989.
Gorrieri, R., Roccetti, Towards Performance Evaluation in Process Algebras (Extended Abstract) Proc. AMAST 93, 1993.
Gunawardena, J., Min-Max Functions, To appear in Discrete Event Dynamic Systems, 1994.
Gunawardena, J., A Dynamic Approach to Timed Behaviours, CONCUR'94, LNCS 836, 178–193, 1994.
Milner, R., Communication and Concurrency, Prentice Hall, 1989.
Olderog, E-R., Operational Petri Nets Semantics for CCSP, Advances in Petri Nets, LNCS 266, 1987.
Plotkin, G. Lattice-Theoretic Properties of Subsumption. Memo MI-R-77, University of Edinburgh, 1970.
Plotkin, G. A Structured Approach to Operational Semantics, DAIMI FN-19, Computer Science Dept., University of Aarhus, 1981.
Rabinovich, A., Trakhtenbrot, B., Behaviour Structures and Nets, Fundamenta Informaticae XI, 357–404, 1988.
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Ferrari, G., Montanari, U. (1995). Dynamic matrices and the cost analysis of concurrent programs. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_61
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DOI: https://doi.org/10.1007/3-540-60043-4_61
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