{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T16:03:02Z","timestamp":1742400182501},"publisher-location":"Berlin, Heidelberg","reference-count":39,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540222361"},{"type":"electronic","value":"9783540277934"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-27793-4_2","type":"book-chapter","created":{"date-parts":[[2010,9,5]],"date-time":"2010-09-05T22:49:31Z","timestamp":1283726971000},"page":"17-34","source":"Crossref","is-referenced-by-count":15,"title":["Reachability Set Generation for Petri Nets: Can Brute Force Be Smart?"],"prefix":"10.1007","author":[{"given":"Gianfranco","family":"Ciardo","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"2_CR1","doi-asserted-by":"crossref","unstructured":"Agerwala, T.: A complete model for representing the coordination of asynchronous processes. Hopkins Computer Research Report 32, Johns Hopkins University, Baltimore, Maryland (July 1974)","DOI":"10.2172\/4242290"},{"key":"2_CR2","volume-title":"Modelling with Generalized Stochastic Petri Nets","author":"M. Ajmone Marsan","year":"1995","unstructured":"Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. John Wiley & Sons, New York (1995)"},{"key":"2_CR3","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/0304-3975(76)90067-0","volume":"3","author":"T. Araki","year":"1977","unstructured":"Araki, T., Kasami, T.: Some decision problems related to the reachability problem for Petri nets. Theoretical Computer Science\u00a03, 85\u2013104 (1977)","journal-title":"Theoretical Computer Science"},{"issue":"3","key":"2_CR4","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1145\/136035.136043","volume":"24","author":"R.E. Bryant","year":"1992","unstructured":"Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Comp. Surv.\u00a024(3), 293\u2013318 (1992)","journal-title":"ACM Comp. Surv."},{"issue":"3","key":"2_CR5","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1287\/ijoc.12.3.203.12634","volume":"12","author":"P. Buchholz","year":"2000","unstructured":"Buchholz, P., Ciardo, G., Donatelli, S., Kemper, P.: Complexity of memory-efficient Kronecker operations with applications to the solution of Markov models. INFORMS J. Comp.\u00a012(3), 203\u2013222 (2000)","journal-title":"INFORMS J. Comp."},{"key":"2_CR6","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1109\/PNPM.1995.524313","volume-title":"Proc. 6th Int. Workshop on Petri Nets and Performance Models (PNPM 1995)","author":"P. Buchholz","year":"1995","unstructured":"Buchholz, P., Kemper, P.: Numerical analysis of stochastic marked graphs. In: Proc. 6th Int. Workshop on Petri Nets and Performance Models (PNPM 1995), Durham, NC, October 1995, pp. 32\u201341. IEEE Comp. Soc. Press, Los Alamitos (1995)"},{"key":"2_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/3-540-58152-9_11","volume-title":"Application and Theory of Petri Nets 1994","author":"G. Ciardo","year":"1994","unstructured":"Ciardo, G.: Petri nets with marking-dependent arc multiplicity: properties and analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol.\u00a0815, pp. 179\u2013198. Springer, Heidelberg (1994)"},{"key":"2_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/978-3-540-45232-4_6","volume-title":"Computer Performance Evaluations. Modelling Techniques and Tools","author":"G. Ciardo","year":"2003","unstructured":"Ciardo, G., Jones, R.L., Miner, A.S., Siminiceanu, R.: Logical and stochastic modeling with SMART. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol.\u00a02794, pp. 78\u201397. Springer, Heidelberg (2003)"},{"key":"2_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/3-540-44988-4_8","volume-title":"Application and Theory of Petri Nets 2000","author":"G. Ciardo","year":"2000","unstructured":"Ciardo, G., Luettgen, G., Siminiceanu, R.: Efficient symbolic state-space construction for asynchronous systems. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol.\u00a01825, pp. 103\u2013122. Springer, Heidelberg (2000)"},{"key":"2_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1007\/3-540-45319-9_23","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"G. Ciardo","year":"2001","unstructured":"Ciardo, G., Luettgen, G., Siminiceanu, R.: Saturation: An efficient iteration strategy for symbolic state space generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol.\u00a02031, pp. 328\u2013342. Springer, Heidelberg (2001)"},{"key":"2_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/3-540-36577-X_27","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"G. Ciardo","year":"2003","unstructured":"Ciardo, G., Marmorstein, R., Siminiceanu, R.: Saturation unbound. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol.\u00a02619, pp. 379\u2013393. Springer, Heidelberg (2003)"},{"key":"2_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/BFb0022196","volume-title":"Computer Performance Evaluation Modelling Techniques and Tools","author":"G. Ciardo","year":"1997","unstructured":"Ciardo, G., Miner, A.S.: Storage alternatives for large structured state spaces. In: Marie, R., Plateau, B., Calzarossa, M.C., Rubino, G.J. (eds.) TOOLS 1997. LNCS, vol.\u00a01245, pp. 44\u201357. Springer, Heidelberg (1997)"},{"key":"2_CR13","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1109\/PNPM.1999.796529","volume-title":"Proc. 8th Int. Workshop on Petri Nets and Performance Models (PNPM 1999)","author":"G. Ciardo","year":"1999","unstructured":"Ciardo, G., Miner, A.S.: A data structure for the efficient Kronecker solution of GSPNs. In: Buchholz, P. (ed.) Proc. 8th Int. Workshop on Petri Nets and Performance Models (PNPM 1999), Zaragoza, Spain, September 1999, pp. 22\u201331. IEEE Comp. Soc. Press, Los Alamitos (1999)"},{"key":"2_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/3-540-36126-X_16","volume-title":"Formal Methods in Computer-Aided Design","author":"G. Ciardo","year":"2002","unstructured":"Ciardo, G., Siminiceanu, R.: Using edge-valued decision diagrams for symbolic generation of shortest paths. In: Aagaard, M.D., O\u2019Leary, J.W. (eds.) FMCAD 2002. LNCS, vol.\u00a02517, pp. 256\u2013273. Springer, Heidelberg (2002)"},{"key":"2_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1007\/978-3-540-45069-6_4","volume-title":"Computer Aided Verification","author":"G. Ciardo","year":"2003","unstructured":"Ciardo, G., Siminiceanu, R.: Structural symbolic CTL model checking of asynchronous systems. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol.\u00a02725, pp. 40\u201353. Springer, Heidelberg (2003)"},{"issue":"1","key":"2_CR16","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/0166-5316(93)90026-Q","volume":"18","author":"G. Ciardo","year":"1993","unstructured":"Ciardo, G., Trivedi, K.S.: A decomposition approach for stochastic reward net models. Perf. Eval.\u00a018(1), 37\u201359 (1993)","journal-title":"Perf. Eval."},{"key":"2_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/3-540-48683-6_44","volume-title":"Computer Aided Verification","author":"A. Cimatti","year":"1999","unstructured":"Cimatti, A., Clarke, E., Giunchiglia, F., Roveri, M.: NuSMV: A new symbolic model verifier. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol.\u00a01633, pp. 495\u2013499. Springer, Heidelberg (1999)"},{"key":"2_CR18","unstructured":"Colom, J.M., Silva, M.: Convex geometry and semiflows in P\/T nets: A comparative study of algorithms for the computation of minimal p-semiflows. In: 10th Int. Conf. on Application and Theory of Petri Nets, Bonn, Germany, pp. 74\u201395 (1989)"},{"key":"2_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1007\/3-540-46429-8_25","volume-title":"Computer Performance Evaluation. Modelling Techniques and Tools","author":"D. Daly","year":"2000","unstructured":"Daly, D., Deavours, D.D., Doyle, J.M., Webster, P.G., Sanders, W.H.: M\u00f6bius: An Extensible Tool for Performance and Dependability Modeling. In: Haverkort, B.R., Bohnenkamp, H.C., Smith, C.U. (eds.) TOOLS 2000. LNCS, vol.\u00a01786, pp. 332\u2013336. Springer, Heidelberg (2000)"},{"key":"2_CR20","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1109\/TC.1981.1675863","volume":"C-30","author":"M. Davio","year":"1981","unstructured":"Davio, M.: Kronecker products and shuffle algebra. IEEE Trans. Comp\u00a0C-30, 116\u2013125 (1981)","journal-title":"IEEE Trans. Comp"},{"key":"2_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1007\/3-540-58152-9_15","volume-title":"Application and Theory of Petri Nets 1994","author":"S. Donatelli","year":"1994","unstructured":"Donatelli, S.: Superposed generalized stochastic Petri nets: definition and efficient solution. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol.\u00a0815, pp. 258\u2013277. Springer, Heidelberg (1994)"},{"issue":"5","key":"2_CR22","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/BF01211911","volume":"8","author":"S. Graf","year":"1996","unstructured":"Graf, S., Steffen, B., Luttgen, G.: Compositional minimisation of finite state systems using interface specifications. Formal Asp. of Comp.\u00a08(5), 607\u2013616 (1996)","journal-title":"Formal Asp. of Comp."},{"key":"2_CR23","unstructured":"Hack, M.: Decidability questions for Petri nets. Technical Report 161, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA (June 1976)"},{"key":"2_CR24","series-title":"IFIP Transactions","first-page":"49","volume-title":"Int. Conference on Very Large Scale Integration","author":"J.R. Burch","year":"1991","unstructured":"Burch, J.R., Clarke, E.M., Long, D.E.: Symbolic model checking with partitioned transition relations. In: Halaas, A., Denyer, P.B. (eds.) Int. Conference on Very Large Scale Integration, Edinburgh, Scotland, August 1991. IFIP Transactions, pp. 49\u201358. North-Holland, Amsterdam (1991)"},{"key":"2_CR25","unstructured":"Kam, T.: State Minimization of Finite State Machines using Implicit Techniques. PhD thesis, University of California at Berkeley (1995)"},{"issue":"1-2","key":"2_CR26","first-page":"9","volume":"4","author":"T. Kam","year":"1998","unstructured":"Kam, T., Villa, T., Brayton, R., Sangiovanni-Vincentelli, A.: Multi-valued decision diagrams: theory and applications. Multiple-Valued Logic\u00a04(1-2), 9\u201362 (1998)","journal-title":"Multiple-Valued Logic"},{"key":"2_CR27","doi-asserted-by":"crossref","unstructured":"Miner, A.S.: Efficient Solution of GSPNs using canonical matrix diagrams. In: Proc. 9th Int. Workshop on Petri Nets and Performance Models, Aachen, Germany, September 2001, pp. 101\u2013110 (2001)","DOI":"10.1109\/PNPM.2001.953360"},{"key":"2_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/3-540-48745-X_2","volume-title":"Application and Theory of Petri Nets 1999","author":"A.S. Miner","year":"1999","unstructured":"Miner, A.S., Ciardo, G.: Efficient reachability set generation and storage using decision diagrams. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol.\u00a01639, pp. 6\u201325. Springer, Heidelberg (1999)"},{"issue":"4","key":"2_CR29","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1109\/5.24143","volume":"77","author":"T. Murata","year":"1989","unstructured":"Murata, T.: Petri Nets: properties, analysis and applications. Proc. of the IEEE\u00a077(4), 541\u2013579 (1989)","journal-title":"Proc. of the IEEE"},{"issue":"5","key":"2_CR30","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1109\/12.926158","volume":"50","author":"E. Pastor","year":"2001","unstructured":"Pastor, E., Cortadella, J., Roig, O.: Symbolic analysis of bounded Petri nets. IEEE Trans. Comp.\u00a050(5), 432\u2013448 (2001)","journal-title":"IEEE Trans. Comp."},{"key":"2_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1007\/3-540-58152-9_23","volume-title":"Application and Theory of Petri Nets 1994","author":"E. Pastor","year":"1994","unstructured":"Pastor, E., Roig, O., Cortadella, J., Badia, R.: Petri net analysis using boolean manipulation. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol.\u00a0815, pp. 416\u2013435. Springer, Heidelberg (1994)"},{"key":"2_CR32","unstructured":"Petri, C.: Kommunikation mit Automaten. PhD thesis, University of Bonn, Bonn, West Germany (1962)"},{"key":"2_CR33","doi-asserted-by":"crossref","unstructured":"Plateau, B.: On the stochastic structure of parallelism and synchronisation models for distributed algorithms. In: Proc. ACM SIGMETRICS, Austin, TX, USA, May 1985, pp. 147\u2013153 (1985)","DOI":"10.1145\/317795.317819"},{"key":"2_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/3-540-60029-9_50","volume-title":"Application and Theory of Petri Nets 1995","author":"O. Roig","year":"1995","unstructured":"Roig, O., Cortadella, J., Pastor, E.: Verification of asynchronous circuits by BDD-based model checking of Petri nets. In: DeMichelis, G., D\u00edaz, M. (eds.) ICATPN 1995. LNCS, vol.\u00a0935, pp. 374\u2013391. Springer, Heidelberg (1995)"},{"key":"2_CR35","doi-asserted-by":"crossref","unstructured":"Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proc. IEEE Int. Conf. on Computer-Aided Design, November 1993, pp. 139\u2013144 (1993)","DOI":"10.1109\/ICCAD.1993.580029"},{"key":"2_CR36","unstructured":"Somenzi, F.: CUDD: CU Decision Diagram Package, Release 2.3.1., http:\/\/vlsi.colorado.edu\/~fabio\/CUDD\/cuddIntro.html"},{"key":"2_CR37","series-title":"Lecture Notes in Computer Science","volume-title":"Algorithms and Computation","author":"S. Tani","year":"1993","unstructured":"Tani, S., Hamaguchi, K., Yajima, S.: The complexity of the optimal variable ordering problems of shared binary decision diagrams. In: Ng, K.W., Balasubramanian, N.V., Raghavan, P., Chin, F.Y.L. (eds.) ISAAC 1993. LNCS, vol.\u00a0762. Springer, Heidelberg (1993)"},{"key":"2_CR38","series-title":"Lecture Notes in Computer Science","first-page":"527","volume-title":"Mathematical Foundations of Computer Science 1978","author":"R. Valk","year":"1978","unstructured":"Valk, R.: On the computational power of extended Petri nets. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol.\u00a064, pp. 527\u2013535. Springer, Heidelberg (1978)"},{"key":"2_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/3-540-10856-4_80","volume-title":"Mathematical Foundations of Computer Science 1981","author":"R. Valk","year":"1981","unstructured":"Valk, R.: Generalizations of Petri nets. In: Gruska, J., Chytil, M.P. (eds.) MFCS 1981. LNCS, vol.\u00a0118, pp. 140\u2013155. Springer, Heidelberg (1981)"}],"container-title":["Lecture Notes in Computer Science","Applications and Theory of Petri Nets 2004"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-27793-4_2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T04:20:31Z","timestamp":1605759631000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-27793-4_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004]]},"ISBN":["9783540222361","9783540277934"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-27793-4_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2004]]}}}