Record link: 
http://hdl.handle.net/20.500.12708/188037
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Title: 
The Membership Problem for Hypergeometric Sequences with Quadratic Parameters
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Citation: 
Kenison, G., Nosan, K., Shirmohammadi, M., & Worrell, J. (2023). The Membership Problem for Hypergeometric Sequences with Quadratic Parameters. In A. Dickenstein, E. Tsigaridas, & G. Jeronimo (Eds.), ISSAC ’23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (pp. 407–416). Association for Computing Machinery. https://doi.org/10.1145/3597066.3597121
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Publisher DOI: 
10.1145/3597066.3597121
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Kenison, George 
Nosan, Klara 
Shirmohammadi, Mahsa 
Worrell, James 
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Organisational Unit: 
E192-04 - Forschungsbereich Formal Methods in Systems Engineering 
E192 - Institut für Logic and Computation 
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Published in: 
ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation 
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ISBN: 
9798400700392
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Date (published): 
24-Jul-2023
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Event name: 
ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023 
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Event date: 
24-Jul-2023 - 27-Jul-2023
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Event place: 
Tromso, Norway
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Number of Pages: 
10
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Publisher: 
Association for Computing Machinery, New York
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Keywords: 
Membership Problem; Algebraic algorithms; Reachability
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Abstract: 
Hypergeometric sequences are rational-valued sequences that satisfy first-order linear recurrence relations with polynomial coefficients; that is, a hypergeometric sequence is one that satisfies a recurrence of the form f(n)un = g(n)un − 1 where . In this paper, we consider the Membership Problem for hypergeometric sequences: given a hypergeometric sequence and a target value , determine whether un = t for some index n. We establish decidability of the Membership Problem under the assumption that either (i) f and g have distinct splitting fields or (ii) f and g are monic polynomials that both split over a quadratic extension of . Our results are based on an analysis of the prime divisors of polynomial sequences and appearing in the recurrence relation.
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Project title: 
Automated Reasoning with Theories and Induction for Software Technologies: ERC Consolidator Grant 2020 (European Commission) 
Distribution Recovery for Invariant Generation of Probabilistic Programs: ICT19-018 (WWTF Wiener Wissenschafts-, Forschu und Technologiefonds) 
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Research Areas: 
Computer Science Foundations: 100%
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Science Branch: 
1020 - Informatik: 80%
1010 - Mathematik: 20%
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Appears in Collections:
Conference Paper

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