Theoretical Computer Science
The direct simulation of Minsky machines in linear logic
Proceedings of the workshop on Advances in linear logic
BI as an assertion language for mutable data structures
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Reachability Analysis of Pushdown Automata: Application to Model-Checking
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
The semantics of BI and resource tableaux
Mathematical Structures in Computer Science
Classical BI: a logic for reasoning about dualising resources
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Exploring the relation between intuitionistic bi and boolean bi: An unexpected embedding
Mathematical Structures in Computer Science
The Undecidability of Boolean BI through Phase Semantics
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Expressivity properties of Boolean BI through relational models
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Nondeterministic Phase Semantics and the Undecidability of Boolean BI
ACM Transactions on Computational Logic (TOCL)
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Recently, Brotherston & Kanovich, and independently Larchey-Wendling & Galmiche, proved the undecidability of the bunched implication logic BBI. Moreover, Brotherston & Kanovich also proved the undecidability of the related logic CBI, as well as its neighbours. All of the above results are based on encodings of two-counter Minsky machines, but are derived using different techniques. Here, we show that the technique of Larchey-Wendling & Galmiche can also be extended, via group Kripke semantics, to prove the undecidability of CBI. Hence, we propose an alternative direct simulation of Minsky machines into both BBI and CBI. We identify a fragment called elementary Boolean BI (eBBI) which is common to the BBI/CBI families of logics and we show that the problem of Minsky machine acceptance can be encoded into eBBI. The soundness of the encoding is derived from the soundness of a goal directed sequent calculus designed for eBBI. The faithfulness of the encoding is obtained from a Kripke model based on the free commutative group Z^n.