2013 Fiscal Year Final Research Report
Semantics of Programming Languages and Quantum Topology
| Project/Area Number |
23500016
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | ソフトウェア / プログラム理論 / プログラム意味論 / トポロジー / 量子不変量 |
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| Research Abstract |
Traced monoidal categories and ribbon categories have been commonly used in semantics of programming languages and quantum topology. However, no concrete example of relating these two areas were not known before. Through this research project, we have constructed such examples by applying ideas and techniques of quantum topology to the categories used in semantics.
Specifically, in categories like Rel, we obtained ribbon Hopf algebras via quantum double construction, and derived ribbon categories with non-trivial braidings. On the other hand, we also discovered that such a construction cannot be done for categories of sequential games, in which no non-trivial Hopf algebra exists.
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