Theoretical Computer Science
ACM Transactions on Computer Systems (TOCS)
Logic programming in a fragment of intuitionistic linear logic
Papers presented at the IEEE symposium on Logic in computer science
The direct simulation of Minsky machines in linear logic
Proceedings of the workshop on Advances in linear logic
The undecidability of second order multiplicative linear logic
Information and Computation
Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Using encryption for authentication in large networks of computers
Communications of the ACM
Introduction to the Theory of Computation: Preliminary Edition
Introduction to the Theory of Computation: Preliminary Edition
Decidability of Linear Affine Logic
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
A Meta-Notation for Protocol Analysis
CSFW '99 Proceedings of the 12th IEEE workshop on Computer Security Foundations
Relating Strands and Multiset Rewriting for Security Protocol Analysis
CSFW '00 Proceedings of the 13th IEEE workshop on Computer Security Foundations
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The most fundamental results of monadic second-order decidability, beyond the decidability of just pure monadic second-order logic, deal with the decidability of the monadic second-order theories of one and two successors and the decidability of the monadic second-order theory of linear order (Büchi, Rabin). Having moved from sets to multisets, we refine the underlying logic as linear logic. In contrast to the classical results, we prove the undecidability of just pure monadic linear logic, even if we use nothing but Horn formulas built up of unary predicates, in which no functional symbols are present. As for affine logic (linear logic plus weakening), we prove the undecidability of the Horn fragment of affine logic, which involves only one binary predicate ("linear order") and a fixed finite number of unary predicates, and which contains no functional symbols at all. We also show the undecidability of the ∃-free Horn fragment of monadic affine logic in the presence of only one constant symbol ("zero") and only one unary functional symbol ("successor"), and a fixed finite number of unary predicate symbols. Along these lines, we obtain the undecidability of the optimistic protocol completion even for the class of communication protocols with two participants such that either of them is a finite automaton provided with one register capable of storing one atomic message, all the predicates used are at most unary, and no compound messages are in the use.