Michael Blondin, Matthias Englert, A. Finkel, Stefan Göller, C. Haase, R. Lazic, P. McKenzie, Patrick Totzke
{"title":"The Reachability Problem for Two-Dimensional Vector Addition Systems with States","authors":"Michael Blondin, Matthias Englert, A. Finkel, Stefan Göller, C. Haase, R. Lazic, P. McKenzie, Patrick Totzke","doi":"10.1145/3464794","DOIUrl":null,"url":null,"abstract":"We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether the numbers in the input are encoded in unary or binary. As a key underlying technical result, we show that, if a configuration is reachable, then there exists a witnessing path whose sequence of transitions is contained in a bounded language defined by a regular expression of pseudo-polynomially bounded length. This, in turn, enables us to prove that the lengths of minimal reachability witnesses are pseudo-polynomially bounded.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"97 1","pages":"1 - 43"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the ACM (JACM)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3464794","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether the numbers in the input are encoded in unary or binary. As a key underlying technical result, we show that, if a configuration is reachable, then there exists a witnessing path whose sequence of transitions is contained in a bounded language defined by a regular expression of pseudo-polynomially bounded length. This, in turn, enables us to prove that the lengths of minimal reachability witnesses are pseudo-polynomially bounded.