Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On The Complexity of Counter Reachability Games   Counter reachability games are played by two players on a graph with labelled
edges. Each move consists in picking an edge from the current location and
adding its label to a counter vector. The objective is to reach a given counter
value in a given location. We distinguish three semantics for counter
reachability games, according to what happens when a counter value would become
negative: the edge is either disabled, or enabled but the counter value becomes
zero, or enabled. We consider the problem of deciding the winner in counter
reachability games and show that, in most cases, it has the same complexity
under all semantics. Surprisingly, under one semantics, the complexity in
dimension one depends on whether the objective value is zero or any other
integer.

4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess