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Communication Dans Un Congrès Année : 2022

Decision Problems for Linear Logic with Least and Greatest Fixed Points

Résumé

Linear logic is an important logic for modelling resources and decomposing computational interpretations of proofs. Decision problems for fragments of linear logic exhibiting "infinitary" behaviour (such as exponentials) are notoriously complicated. In this work, we address the decision problems for variations of linear logic with fixed points (µMALL), in particular, recent systems based on "circular" and "non-wellfounded" reasoning. In this paper, we show that µMALL is undecidable. More explicitly, we show that the general non-wellfounded system is Π01-hard via a reduction to the non-halting of Minsky machines, and thus is strictly stronger than its circular counterpart (which is in Σ01). Moreover, we show that the restriction of these systems to theorems with only the least fixed points is already Σ01-complete via a reduction to the reachability problem of alternating vector addition systems with states. This implies that both the circular system and the finitary system (with explicit (co)induction) are Σ01-complete.
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Dates et versions

hal-03867393 , version 1 (23-11-2022)

Identifiants

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Anupam Das, Abhishek De, Alexis Saurin. Decision Problems for Linear Logic with Least and Greatest Fixed Points. 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022), Aug 2022, Haifa, Israel. ⟨10.4230/LIPIcs.FSCD.2022.20⟩. ⟨hal-03867393⟩
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