PSPACE-Completeness of a Thread Criterion for Cyclic Proofs in Linear Logic with Least and Greatest Fixed Points

International audienceIn the context of logics with least and greatest fixed points, circular (ie. non-wellfounded but regular) proofs have been proposed as an alternative to induction and coinduction with explicit invariants. However, those proofs are not wellfounded and to recover logical consistency, it is necessary to consider a validity criterion which differentiates valid proofs among all preproofs (i.e. infinite derivation trees). The paper focuses on circular proofs for MALL with fixed points. It is known that given a finite circular representation of a non-wellfounded preproof, one can decide in PSPACE whether this preproof is valid with respect to the thread criterion. We prove that the problem of deciding thread-validity for µMALL is in fact PSPACE-complete.Our proof is based on a deeper exploration of the connection between thread-validity and the size-change termination principle, which is usually used to ensure program termination