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The Skolem Problem in rings of positive characteristic
- Speaker(s)
- Ruiwen Dong
- Affiliation
- University of Oxford
- Language of the talk
- English
- Date
- April 1, 2026, 2:15 p.m.
- Room
- room 5440
- Title in Polish
- The Skolem Problem in rings of positive characteristic
- Seminar
- Seminar Automata Theory
The Skolem Problem in a commutative ring R asks, given a linear recurrence sequence over R, decide whether it contains a zero term. Decidability of the Skolem Problem over ring of characteristic zero (such as integers) is a longstanding open problem. In this talk we show its decidability over rings of positive characteristic, extending Derksen's (2007) result over fields of prime characteristic. Our main tool is an automata-based method which computes the base-p expansion of the solution sets.
This is based on joint work with Doron Shafrir.
The Skolem Problem in a commutative ring R asks, given a linear recurrence sequence over R, decide whether it contains a zero term. Decidability of the Skolem Problem over ring of characteristic zero (such as integers) is a longstanding open problem. In this talk we show its decidability over rings of positive characteristic, extending Derksen's (2007) result over fields of prime characteristic. Our main tool is an automata-based method which computes the base-p expansion of the solution sets.
This is based on joint work with Doron Shafrir.
