Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Blondin et al. shod 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.  ansr 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.
['Matthias Englert', 'Ranko Lazic', 'Patrick Totzke']
I am writing a research paper on a idea Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete
[{"from": "human", "value": "I am writing a research paper on a idea Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Blondin et al. shod 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.  ansr 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."}]