We study first-order definability in the lattice L of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable in L . As examples, if T is either the equational theory of a finite semigroup or a finitely axiomatizable locally finite theory, then the set {T, T } is definable, where T ∂ is the dual theory obtained by invertin...

We consider the problem of constructing a minimal cycle-breaking set of turns for a given undirected graph. This problem is important for deadlock-free wormhole routing in computer and communication networks, such as Networks of Workstations. The proposed Cycle Breaking algorithm, or CB algorithm, guarantees that the constructed set of prohibited turns is minimal and that the fraction of the pr...

Complete axiomatizations and exponential-time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents. The results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are finitely many agents, provided that we can check the cardinality of certain set differences G − G′...

In this article, we prove that (unit sphere, non-harmonic cone) is a Heisenberg uniqueness pair for the symplectic Fourier transform on C n . We derive spheres as well cones are determining sets spectral projections of finite measure supported unit sphere. Further, if finitely function step two nilpotent Lie group arbitrary rank, then must be zero. The latter result correlates to annihilating W...

Finitely Supported Mathematics represents a part of mathematics for experimental sciences which has a continuous evolution in the last century. It is developed according to the Fraenkel-Mostowski axioms of set theory. The axiom of choice is inconsistent in the Finitely Supported Mathematics. We prove that several weaker forms of the axiom of choice are also inconsistent in the Finitely Supporte...

We give a new characterization of biinfinite Sturmian sequences in terms indistinguishable asymptotic pairs. Two on full Z-shift are if the sets occurrences every pattern each sequence coincide up to finitely supported permutation. This can be seen as an extension Pirillo’s theorem which characterizes Christoffel words. Furthermore, we provide pairs arbitrary alphabets using substitutions and c...

The theory of finitely supported structures is used for dealing with very large sets having a certain degree symmetry. This framework generalizes the classical set Zermelo-Fraenkel by allowing infinitely many basic elements no internal structure (atoms) and equipping group actions permutation over these elements. On other hand, soft represent generalization fuzzy to deal uncertainty in parametr...