Mikołaj Bojańczyk
ABSTRACT
We propose a definition for computable functions on hereditarily definable sets. Such sets are possibly infinite data structures that can be defined using a fixed underlying logical structure, such as (N, =). We show that, under suitable assumptions on the underlying structure, a programming language called definable while programs captures exactly the computable functions. Next, we introduce a complexity class called fixed-dimension polynomial time, which intuitively speaking describes polynomial computation on hereditarily definable sets. We show that this complexity class contains all functions computed by definable while programs with suitably defined resource bounds. Proving the converse inclusion would prove that Choiceless Polynomial Time with Counting captures polynomial time on finite graphs.
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- Mikołaj Bojańczyk. 2011. Data Monoids. In 28th International Symposium on Theoretical Aspects of Computer Science, STACS2011, March 10-12, 2011, Dortmund, Germany. 105--116.Google Scholar
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- Mikołaj Bojańczyk, Bartek Klin, and Slawomir Lasota. 2011. Automata with Group Actions. In Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011, June 21-24, 2011, Toronto, Ontario, Canada. 355--364. Google ScholarDigital Library
- Mikołaj Bojańczyk and Szymon Torúczyk. 2012. Imperative Programming in Sets with Atoms. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2012, December 15-17, 2012, Hyderabad, India. 4--15.Google Scholar
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- Eryk Kopczynski and Szymon Torúczyk. 2017. LOIS: syntax and semantics. In Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages, POPL 2017, Paris, France, January 18-20, 2017. 586--598. Google ScholarDigital Library
- Andrew M. Pitts. 2013. Nominal Sets: Names and Symmetry in Computer Science. Cambridge University Press, New York, NY, USA. Google ScholarCross Ref
- Benjamin Rossman. 2010. Choiceless Computation and Symmetry. Springer Berlin Heidelberg, Berlin, Heidelberg, 565--580. Google ScholarDigital Library
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