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SUMMARY:James Rooney (McMaster University\, Canada)
DTSTART:20220301T200000Z
DTEND:20220301T210000Z
DTSTAMP:20260423T004134Z
UID:PALS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PALS/30/">No
 nlinear idempotent Mal'tsev Condition Satisfaction Problems: why semilatti
 ces are hard and lattices are easier</a>\nby James Rooney (McMaster Univer
 sity\, Canada) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAb
 stract\nIn their 2020 article "Deciding some Mal'tsev conditions in finite
  idempotent algebras" Kazda and Valeriote conjecture that for a linear str
 ong Mal'tsev condition the associated idempotent Mal'tsev condition satisf
 action problem (MCSP) will always be polynomial-time decidable. In an earl
 ier-published 2019 article Freese\, Nation and Valeriote showed that testi
 ng for a semilattice term (a nonlinear condition) is EXPTIME-complete even
  for idempotent algebras. \n\nWhile preparing my PhD thesis I investigated
  the hypothesis that nonlinear Mal'tsev conditions might always be EXPTIME
 -complete to detect. I was able to prove that there are nonlinear Mal'tsev
  conditions whose related idempotent MCSPs are in the class NP. Assuming t
 hat NP is not EXPTIME this provides the first examples of nonlinear Mal'ts
 ev conditions whose idempotent MCSPs are not EXPTIME-complete. The existen
 ce of lattice terms is one such example.\n\nIn this talk we briefly revisi
 t the 2019 result of Freese\, Nation and Valeriote before sketching the de
 tails of my proof that detection of lattice terms in an idempotent algebra
  is an NP problem.\n
LOCATION:https://researchseminars.org/talk/PALS/30/
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