The geometry of semaphore programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
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Modeling concurrency with geometry
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Journal of the ACM (JACM)
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Journal of the ACM (JACM)
Distributed Algorithms
Durations for Truly-Concurrent Transitions
ESOP '96 Proceedings of the 6th European Symposium on Programming Languages and Systems
ECHIDNA: A System for Manipulating Explicit Choice Higher Dimensional Automata
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
Dihomotopy as a Tool in State Space Analysis
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
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TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
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Homology of Higher Dimensional Automata
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Semantics and Analysis of Linda-Based Languages
WSA '93 Proceedings of the Third International Workshop on Static Analysis
Extraction of Concurrent Processes from Higher Dimensional Automata
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
Higher Dimensional Transition Systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Complete Cuboidal Sets in Axiomatic Domain Theory
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Categories of asynchronous systems
Categories of asynchronous systems
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Mathematical Structures in Computer Science
Homotopy invariants of higher dimensional categories and concurrency in computer science
Mathematical Structures in Computer Science
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CONCUR 2005 - Concurrency Theory
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Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
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ACM Transactions on Autonomous and Adaptive Systems (TAAS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
Comparing Topological Models for Concurrency
Electronic Notes in Theoretical Computer Science (ENTCS)
A Fibration Category of Local Pospaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Criteria for Homotopic Maps to be So Along Monotone Homotopies
Electronic Notes in Theoretical Computer Science (ENTCS)
Sheaves and Geometric Logic and Applications to Modular Verification of Complex Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
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SAFECOMP'11 Proceedings of the 30th international conference on Computer safety, reliability, and security
Trace spaces: an efficient new technique for state-space reduction
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Simplicial Models for Concurrency
Electronic Notes in Theoretical Computer Science (ENTCS)
Formal Relationships Between Geometrical and Classical Models for Concurrency
Electronic Notes in Theoretical Computer Science (ENTCS)
Streams, d-Spaces and Their Fundamental Categories
Electronic Notes in Theoretical Computer Science (ENTCS)
History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps
Electronic Notes in Theoretical Computer Science (ENTCS)
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We show in this article that some concepts from homotopy theory, in algebraic topology, are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to "elastic deformation" or homotopy, giving information about important properties of the program, such as deadlocks, unreachables, serializability, essential schedules, etc. In fact, it is not quite ordinary homotopy that has to be used, but rather a "directed homotopy" that does not reverse the flow of time. We show some of the essential differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two-phase protocol, well-known and used in concurrent database theory. We end up with a list of problems from both a mathematical and a computer-scientific point of view.