Via an encoding of the Modified Post’s Correspondence Problem, this paper shows that it is undecidable whether an automatic semigroup is cancellative.

Let R be a commutative Noetherian ring of dimension d and M cancellative torsion-free seminormal monoid. Then: (1) A type R[d,m,n] P projective A[M]-module rank r≥max {2,d+1}. Then the action E(A[M]⊕P) on (A[M]⊕P) is transitive (2) Assume (R,m,K) regular local containing field k such that either char k=0 or k=p tr-deg K∕

Starting from a decomposition result of MTL-chains as ordinal sums, we focus our attention on a particular kind of indecomposable semihoops, namely weakly cancellative semihoops. Weak cancellation property is proved to be the difference between cancellation and pseudocomplementation, so it gives a new axiomatization of Product logic and ΠMTL. By adding this property, some new fuzzy logics (prop...

By de ning a notion of cancellation in algebraic circuits, we study the power of negation at a ner granularity than previously considered. Our result is that in the absence of cancellation, computing the determinant requires exponential circuit size. Previous work shows that cancellations are essential for e ciently computing certain monotone (all coe cients positive) polynomials. The work pres...