{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T10:57:14Z","timestamp":1791197834747,"version":"4.1.0"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319114385","type":"print"},{"value":"9783319114392","type":"electronic"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-11439-2_9","type":"book-chapter","created":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T01:30:11Z","timestamp":1410744611000},"page":"112-124","source":"Crossref","is-referenced-by-count":28,"title":["Integer Vector Addition Systems with States"],"prefix":"10.1007","author":[{"given":"Christoph","family":"Haase","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simon","family":"Halfon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"issue":"1-2","key":"9_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.tcs.2007.10.025","volume":"391","author":"P. Bell","year":"2008","unstructured":"Bell, P., Potapov, I.: On undecidability bounds for matrix decision problems. Theor. Comput. Sci.\u00a0391(1-2), 3\u201313 (2008)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR2","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1090\/S0002-9939-1976-0396605-3","volume":"55","author":"I. Borosh","year":"1976","unstructured":"Borosh, I., Treybing, L.B.: Bounds on positive integral solutions of linear Diophantine equations. Proc. AMS\u00a055, 299\u2013304 (1976)","journal-title":"Proc. AMS"},{"key":"9_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/978-3-642-40313-2_22","volume-title":"Mathematical Foundations of Computer Science 2013","author":"P. Buckheister","year":"2013","unstructured":"Buckheister, P., Zetzsche, G.: Semilinearity and context-freeness of languages accepted by valence automata. In: Chatterjee, K., Sgall, J. (eds.) MFCS 2013. LNCS, vol.\u00a08087, pp. 231\u2013242. Springer, Heidelberg (2013)"},{"key":"9_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/BFb0055044","volume-title":"Automata, Languages and Programming","author":"C. Dufourd","year":"1998","unstructured":"Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol.\u00a01443, pp. 103\u2013115. Springer, Heidelberg (1998)"},{"issue":"1","key":"9_CR5","doi-asserted-by":"crossref","first-page":"13","DOI":"10.3233\/FI-1997-3112","volume":"31","author":"J. Esparza","year":"1997","unstructured":"Esparza, J.: Petri nets, commutative context-free grammars, and basic parallel processes. Fundam. Inform.\u00a031(1), 13\u201325 (1997)","journal-title":"Fundam. Inform."},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/978-3-642-40313-2_37","volume-title":"Mathematical Foundations of Computer Science 2013","author":"A. Finkel","year":"2013","unstructured":"Finkel, A., G\u00f6ller, S., Haase, C.: Reachability in register machines with polynomial updates. In: Chatterjee, K., Sgall, J. (eds.) MFCS 2013. LNCS, vol.\u00a08087, pp. 409\u2013420. Springer, Heidelberg (2013)"},{"key":"9_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/978-3-642-38697-8_10","volume-title":"Application and Theory of Petri Nets and Concurrency","author":"E. Fraca","year":"2013","unstructured":"Fraca, E., Haddad, S.: Complexity analysis of continuous petri nets. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol.\u00a07927, pp. 170\u2013189. Springer, Heidelberg (2013)"},{"key":"9_CR8","unstructured":"Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)"},{"issue":"2","key":"9_CR9","doi-asserted-by":"publisher","first-page":"285","DOI":"10.2140\/pjm.1966.16.285","volume":"16","author":"S. Ginsburg","year":"1966","unstructured":"Ginsburg, S., Spanier, E.H.: Semigroups, Presburger formulas and languages. Pac. J. Math.\u00a016(2), 285\u2013296 (1966)","journal-title":"Pac. J. Math."},{"issue":"1","key":"9_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0168-0072(89)90023-7","volume":"43","author":"E. Gr\u00e4del","year":"1989","unstructured":"Gr\u00e4del, E.: Dominoes and the complexity of subclasses of logical theories. Ann. Pure Appl. Logic\u00a043(1), 1\u201330 (1989)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"3","key":"9_CR11","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/0304-3975(78)90020-8","volume":"7","author":"S.A. Greibach","year":"1978","unstructured":"Greibach, S.A.: Remarks on blind and partially blind one-way multicounter machines. Theor. Comput. Sci.\u00a07(3), 311\u2013324 (1978)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"Haase, C.: Subclasses of Presburger arithmetic and the weak EXP hierarchy. In: Proc. CSL-LICS (to appear, 2014)","DOI":"10.1145\/2603088.2603092"},{"key":"9_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/978-3-642-04081-8_25","volume-title":"CONCUR 2009 - Concurrency Theory","author":"C. Haase","year":"2009","unstructured":"Haase, C., Kreutzer, S., Ouaknine, J., Worrell, J.: Reachability in succinct and parametric one-counter automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol.\u00a05710, pp. 369\u2013383. Springer, Heidelberg (2009)"},{"issue":"1","key":"9_CR14","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0304-3975(76)90008-6","volume":"2","author":"M. Hack","year":"1976","unstructured":"Hack, M.: The equality problem for vector addition systems is undecidable. Theor. Comput. Sci.\u00a02(1), 77\u201395 (1976)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1007\/978-3-642-22110-1_60","volume-title":"Computer Aided Verification","author":"M. Hague","year":"2011","unstructured":"Hague, M., Lin, A.W.: Model checking recursive programs with numeric data types. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol.\u00a06806, pp. 743\u2013759. Springer, Heidelberg (2011)"},{"issue":"1-2","key":"9_CR16","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0019-9958(85)80015-2","volume":"66","author":"D.T. Huynh","year":"1985","unstructured":"Huynh, D.T.: The complexity of equivalence problems for commutative grammars. Inform. Control\u00a066(1-2), 103\u2013121 (1985)","journal-title":"Inform. Control"},{"issue":"4","key":"9_CR17","first-page":"147","volume":"22","author":"D.T. Huynh","year":"1986","unstructured":"Huynh, D.T.: A simple proof for the ${\\Sigma}^p_2$ upper bound of the inequivalence problem for semilinear sets. Elektron. Inform. Kybernet.\u00a022(4), 147\u2013156 (1986)","journal-title":"Elektron. Inform. Kybernet."},{"issue":"1-2","key":"9_CR18","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/S0304-3975(00)00100-6","volume":"256","author":"P. Jan\u010dar","year":"2001","unstructured":"Jan\u010dar, P.: Nonprimitive recursive complexity and undecidability for Petri net equivalences. Theor. Comput. Sci.\u00a0256(1-2), 23\u201330 (2001)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR19","doi-asserted-by":"crossref","unstructured":"Kopczy\u0144ski, E., To, A.W.: Parikh images of grammars: Complexity and applications. In: Proc. LICS, pp. 80\u201389 (2010)","DOI":"10.1109\/LICS.2010.21"},{"key":"9_CR20","unstructured":"Lipton, R.: The reachability problem is exponential-space-hard. Technical report, Yale University, New Haven, CT (1976)"},{"key":"9_CR21","first-page":"238","volume-title":"Proc. STOC","author":"E.W. Mayr","year":"1981","unstructured":"Mayr, E.W.: An algorithm for the general Petri net reachability problem. In: Proc. STOC, pp. 238\u2013246. ACM, New York (1981)"},{"key":"9_CR22","doi-asserted-by":"crossref","unstructured":"Plandowski, W., Rytter, W.: Complexity of language recognition problems for compressed words. In: Karhum\u00e4ki, J., Maurer, H.A., P\u0103un, G., Rozenberg, G. (eds.) Jewels are Forever, pp. 262\u2013272 (1999)","DOI":"10.1007\/978-3-642-60207-8_23"},{"issue":"2","key":"9_CR23","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/0304-3975(78)90036-1","volume":"6","author":"C. Rackoff","year":"1978","unstructured":"Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comput. Sci.\u00a06(2), 223\u2013231 (1978)","journal-title":"Theor. Comput. Sci."},{"key":"9_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1007\/978-3-642-41036-9_18","volume-title":"Reachability Problems","author":"J. Reichert","year":"2013","unstructured":"Reichert, J.: On the complexity of counter reachability games. In: Abdulla, P.A., Potapov, I. (eds.) RP 2013. LNCS, vol.\u00a08169, pp. 196\u2013208. Springer, Heidelberg (2013)"},{"key":"9_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1007\/978-3-642-15155-2_54","volume-title":"Mathematical Foundations of Computer Science 2010","author":"P. Schnoebelen","year":"2010","unstructured":"Schnoebelen, P.: Revisiting ackermann-hardness for lossy counter machines and reset petri nets. In: Hlin\u011bn\u00fd, P., Ku\u010dera, A. (eds.) MFCS 2010. LNCS, vol.\u00a06281, pp. 616\u2013628. Springer, Heidelberg (2010)"},{"key":"9_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1136","DOI":"10.1007\/978-3-540-27836-8_94","volume-title":"Automata, Languages and Programming","author":"H. Seidl","year":"2004","unstructured":"Seidl, H., Schwentick, T., Muscholl, A., Habermehl, P.: Counting in trees for free. In: D\u00edaz, J., Karhum\u00e4ki, J., Lepist\u00f6, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol.\u00a03142, pp. 1136\u20131149. Springer, Heidelberg (2004)"}],"container-title":["Lecture Notes in Computer Science","Reachability Problems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-11439-2_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T19:01:11Z","timestamp":1676660471000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-11439-2_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319114385","9783319114392"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-11439-2_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}