Regular Intersection Emptiness of Graph Problems: Finding a Needle in a Haystack of Graphs with the Help of Automata
Abstract
The Int_regproblem of a combinatorial problem P asks, given a nondeterministic automaton M as input, whether the language L(M) accepted by M contains any positive instance of the problem P. We consider the Int_regproblem for a number of different graph problems and give general criteria that give decision procedures for these Int_regproblems. To achieve this goal, we consider a natural graph encoding so that the language of all graph encodings is regular. Then, we draw the connection between classical pumping and interchangearguments from the field of formal language theory with the graph operations induced on the encoded graph. Our techniques apply among others to the Int_regproblem of wellknown graph problems like Vertex Cover and Independent Set, as well as to subgraph problems, graphedit problems and graphpartitioning problems, including coloring problems.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.05826
 Bibcode:
 2020arXiv200305826W
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Computation and Language