Barnaby Martin (Durham): The Complexity of Quantified Constraints (School Seminar)

Event details

  • When: 24th October 2017 14:00 - 15:00
  • Where: Cole 1.33a
  • Series: School Seminar Series
  • Format: Seminar

Abstract:

We elaborate the complexity of the Quantified Constraint Satisfaction Problem, QCSP(A), where A is a finite idempotent algebra. Such a problem is either in NP or is co-NP-hard, and the borderline is given precisely according to whether A enjoys the polynomially-generated powers (PGP) property. This reduces the complexity classification problem for QCSPs to that of CSPs, modulo that co-NP-hard cases might have complexity rising up to Pspace-complete. Our result requires infinite languages, but in this realm represents the proof of a slightly weaker form of a conjecture for QCSP complexitymade by Hubie Chen in 2012. The result relies heavily on the algebraic dichotomy between PGP and exponentially-generated powers (EGP), proved by Dmitriy Zhuk in 2015, married carefully to previous work of Chen.

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