Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete
Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete
Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors are given in unary, the improved guess-and-verify algorithm requires only logarithmic space.
- University of Warwick United Kingdom
- UNIVERSITY OF WARWICK
- University of Warwick
- University of Warwick
- University of Edinburgh United Kingdom
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, F.1.1, QA76, Logic in Computer Science (cs.LO)
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, F.1.1, QA76, Logic in Computer Science (cs.LO)
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