Formal languages
Journal of the ACM (JACM)
Programmed Grammars and Classes of Formal Languages
Journal of the ACM (JACM)
Parallel Program Schemata and Maximal Parallelism I. Fundamental Results
Journal of the ACM (JACM)
The Theory of Parsing, Translation, and Compiling
The Theory of Parsing, Translation, and Compiling
Context-free parallel leveled languages
Context-free parallel leveled languages
Formal languages and their relation to automata
Formal languages and their relation to automata
The Mathematical Theory of Context-Free Languages
The Mathematical Theory of Context-Free Languages
Properties of Conflict-Free and Persistent Petri Nets
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
Decidability of reachability in vector addition systems (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
An algorithm for the general Petri net reachability problem
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
The decidability of the reachability problem for vector addition systems (Preliminary Version)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Catalytic P systems, semilinear sets, and vector addition systems
Theoretical Computer Science
Lossy counter machines decidability cheat sheet
RP'10 Proceedings of the 4th international conference on Reachability problems
P systems: some recent results and research problems
UPP'04 Proceedings of the 2004 international conference on Unconventional Programming Paradigms
The power of maximal parallelism in p systems
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
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With geometrical techniques we hope to bring new insight into the reachability problem for vector-addition systems, which is pertaining in many areas in computer science theory but unsolved ever since it was proposed by Karp and Miller. We show that the reachability-problem is decidable in dim. ≤ 3 and give a partial solution for the general problem covering a wide instance of it. In both cases a semi-linear characterization is obtained for the complete set of solutions. Contrary to common belief the complete solution in dim. 3 does not immediately generalize, and our analysis gives evidence why. A few generalizations and application to long-standing classificational problems in language theory are discussed.