Simply typed β-convertibility is TOWER-complete even for safe λ-terms

Nguyễn Lê Thành Dũng
LIP, ÉNS Lyon

Date(s) : 22/06/2023   iCal
11 h 00 min - 12 h 30 min

We consider the following decision problem: given two simply typed λ-terms, are they β-convertible? Equivalently, do they have the same normal form? It is famously non-elementary, but the precise complexity – namely TOWER-complete – is lesser known. The talk will start by explaining what this means.

Our original contribution is to show that the problem stays TOWER-complete when the two input terms belong to Blum and Ong’s safe λ-calculus, a fragment of the simply typed λ-calculus arising from the study of higher-order recursion schemes. Previously, the best known lower bound for this safe β-convertibility problem was PSPACE-hardness. Our proof proceeds by reduction from the star-free expression equivalence problem, taking inspiration from the author’s work with Pradic on « implicit automata in typed λ-calculi ».

Emplacement
Amphi 5 - TPR2 (room 500-504, fifth floor)

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