Given a polynomially bounded o–minimal structure S and a set A ⊂ R belonging to S, we show that A (considered as a subset of C) is pluriregular at every point a ∈ intA that can be attained by a C∞ arc γ : [0, ] → R belonging to S, such that γ(0) = a and γ((0, ]) ⊂ intA. In particular, if S is a recently found in [22] polynomially bounded o–minimal structure of quasianalytic functions in the sen...

We construct an analogue of the Lyndon-HochschildSerre spectral sequence in the context of polynomially bounded cohomology. For G an extension of Q by H, this spectral sequences converges to the polynomially bounded cohomology of G, HP ∗(G). If the extension is a polynomial extension in the sense of Noskov with H and Q isocohomological and Q of type HF∞, the spectral sequence has E 2 -term HP (...

The class of neighbour games is the intersection of the class of assignment games (cf. Shapley and Shubik (1972)) and the class of component additive games (cf. Curiel et al. (1994)). For assignment games and component additive games there exist polynomially bounded algorithms of order p for calculating the nucleolus, where p is the number of players. In this paper we present a polynomially bou...

In recent years, formal verification applications have attracted significant attention. In particular, verification of the security of cryptosystems has been investigated extensively. In this study, we attempt to develop various mathematical libraries for cryptology using the Mizar proof checking system. Polynomially bounded and negligible functions play very important roles in cryptology. Ther...

The perfect matching problem is known to be in ¶, in randomized NC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations. Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent. They showed that for such bipartite ...

Consider a planar graph G = (V,E) with polynomially bounded edge weight function w : E → [0, poly(n)]. The main results of this paper are NC algorithms for the following problems: • minimum weight perfect matching in G, • maximum cardinality and maximum weight matching in G when G is bipartite, • maximum multiple-source multiple-sink flow in G where c : E → [1, poly(n)] is a polynomially bounde...