We apply Stone duality and model theory to study the structure theory of free pro-aperiodic monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be viewed as elementary equivalence classes of pseudofinite words. Model theory provides us with saturated words in each such class, i.e., words in which all possible factorizations are realized. We give several application...

We show that the number of satisfying assignments of a k-CNF formula is determined uniquely from the numbers of unsatisfying assignments for clause-sets of size up to ⌊log k⌋+ 2. The information of this size is also shown to be necessary. key words: combinatorial problems; SAT; k-CNF formula; counting; inclusion-exclusion

We show how to construct a non-2-colorable k-uniform hypergraph with (2) edges. By the duality of hypergraphs and monotone CNF-formulas this gives an unsatisfiable monotone k-CNF with (2) clauses.

We show that a germ of a real analytic Lorentz metric on R3 which is locally homogeneous on an open set containing the origin in its closure is necessarily locally homogeneous. We classifiy Lie algebras that can act quasihomogeneously—meaning they act transitively on an open set admitting the origin in its closure, but not at the origin—and isometrically for such a metric. In the case that the ...

A Boolean formula in a conjunctive normal form is called a (k, s)-formula if every clause contains exactly k variables and every variable occurs in at most s clauses. We show that there are unsatisfiable (k, 4 · 2 k

CutRes is a system which takes as input an LK-proof with arbitrary cuts and skolemized end-sequent and gives as output an LKproof with atomic cuts only. The elimination of cuts is performed in the following way: An unsatisfiable set of clauses C is assigned to a given LK-proof Π. Any resolution refutation ψ of C then serves as a skeleton for an LK-proof Σ of the original end-sequent, containing...

We introduce new biholomorphic invariants for real-analytic hypersurfaces in C and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new invariants, guaranteeing that the stability group is finite, and give (sharp) bounds on the cardinality of the stability group in this case. We also give a sufficient condition for the stabil...

Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ(G), obtained from the Smith normal form of M , and whose order is the number of spanning trees of G. We provide some general results on the relationship between the eigenvalues of M and the structure of Φ(G), and address the question of how often the group Φ(G) is cyclic.

We develop a new method for placing a given context-free grammar into Greibach normal form with only polynomial increase of its size. Starting with an arbitrary "-free context-free grammar G, we transform G into an equivalent context-free grammar H in extended Greibach normal form; i.e., in addition to rules, fulllling the Greibach normal form properties, the grammar can have chain rules. The s...