Distributed graph problems through an automata-theoretic lens

The locality of a graph problem is the smallest distance T such that each node can choose its own part solution based on radius-T neighborhood. In many settings, be solved efficiently with distributed or parallel algorithm if and only it has small locality. this work we seek to automate study solvability locality: given description Π, would like determine Π solvable what asymptotic as function size graph. Put otherwise, automatically synthesize efficient algorithms for solving Π. We focus locally checkable problems; these are problems in which globally feasible looks all constant-radius neighborhoods. Prior brought primarily bad news: questions related undecidable general, even case labeled paths cycles, determining PSPACE-hard (Balliu et al., PODC 2019). complement prior negative results cases unlabeled cycles and, an extension, rooted trees. from automata-theoretic perspective by representing nondeterministic finite automaton M over unary alphabet. identify polynomial-time-computable properties near-completely capture paths, exception one specific co-NP-complete.