Tue, 23 Feb 2021, 1 pm MST

The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP). In a [LICS '19] paper it was shown that a specific PCSP, the problem to find a valid Not-All-Equal solution to a 1-in-3-SAT instance, is not finitely tractable in that it can be solved by a trivial reduction to a tractable CSP, but such a CSP is necessarily over an infinite domain (unless P=NP). We further explore this phenomenon: we give a general necessary condition for finite tractability and characterize finite tractability within a class of templates - the "basic" tractable cases in the dichotomy theorem for symmetric Boolean PCSPs allowing negations by Brakensiek and Guruswami [SODA'18]. This is a joint work with Libor Barto.