2003/06/27 by Elmar Böhler, Böhler, Elmar, Edith Hemaspaandra +5
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Constraint Satisfaction and Optimization #F.1.3 #F.4.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #cs.CC #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0306134
This is the full version of our STACS 2004 paper
openalex publication_date 2003/06/27 · arxiv created 2004/04/12 · arxiv updated 2009/11/30 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems (nowadays usually called Boolean constraint satisfaction problems) and showed that all these satisfiability problems are either in P or NP-complete. In recent years, similar results have been obtained for quite a few other problems for Boolean constraints.Almost all of these problems are variations of the satisfiability problem. In this paper, we address a problem that is not a variation of satisfiability, namely, the isomorphism problem for Boolean constraints. Previous work by Böhler et al. showed that the isomorphism problem is either coNP-hard or reducible to the graph isomorphism problem (a problem that is in NP, but not known to be NP-hard), thus distinguishing a hard case and an easier case. However, they did not classify which cases are truly easy, i.e., in P. This paper accomplishes exactly that. It shows that Boolean constraint isomorphism is coNP-hard (and GI-hard), or equivalent to graph isomorphism, or in P, and it gives simple criteria to determine which case holds.