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Complexity questions on linear logic

To: types, logic

Subject: Complexity questions on linear logic

From: gunter@central.cis.upenn.edu

Date: Sun, 4 Feb 90 17:08:16 EST

InReplyTo: John C. Mitchell's message of Sun, 4 Feb 90 09:40:35 EST <9002041440.AA00818@stork.lcs.mit.edu>

Sender: meyer@theory.lcs.mit.edu
Date: Sun, 4 Feb 90 12:12:33 EST
I'm also curious about the status of the propositional linear logic
decision problem.
Research on connections between Petri nets (vector addition systems)
and fragments of propositional linear logic has shown that the
decision problem for linear logic with the connectives:
o (linear implication) ox (tensor product) ! (of course)
must be at least has hard as the decision problem for forward
markings. Since the latter was a significant topic of research for
some time, it seems that propositional linear logic (with the
modalities) must encode some quite difficult decision problems.
carl gunter