We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko’s framework for polynomial space computability in Rn to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem holds for every weakly pspace-random point.

We investigate the asymptotic version of the Erdős-Ko-Rado theorem for the random kuniform hypergraph H(n, p). For 2 ≤ k(n) ≤ n/2, let N = ( n k ) and D = ( n−k k ) . We show that with probability tending to 1 as n→∞, the largest intersecting subhypergraph of H(n, p) has size (1 + o(1))p k nN , for any p n k ln 2 ( n k ) D−1. This lower bound on p is asymptotically best possible for k = Θ(n). F...

We define and compare several probabilistic notions of computability for mappings from represented spaces (that are equipped with a measure or outer measure) into computable metric spaces. We thereby generalize definitions by [Ko 1991] and Parker (see [Parker 2003, Parker 2005, Parker 2006]), and furthermore introduce the new notion of computability in the mean. Some results employ a notion of ...

The ordering principle states that every finite linear order has a least element. We show that, in the relativized setting, the surjective weak pigeonhole principle for polynomial time functions does not prove a Herbrandized version of the ordering principle over T 2 . This answers an open question raised in [Buss, Ko lodziejczyk and Thapen, 2012] and completes their program to compare the stre...

Let n, d, and k be positive integers such that k ≥ 2, d ≥ 1, and n = kd. Furthermore, let N = {1, . . . , n} be the ground set and B(n, d) = {S ⊆ N : |S| = d} denote the family of all subsets of cardinality d in N ; obviously, |B(n, d)| = ( n d ) . A subfamily P (n, d) ⊆ B(n, d) that consists of k pairwise disjoint subsets is called a partition. Obviously, all sets of B(n, d) participate the sa...

A graph G is called (k, d)∗-choosable if, for every list assignment L satisfying |L(v)| = k for all v ∈ V (G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. Ko-Wei Lih et al. used the way of discharging to prove that every planar graph without 4-cycles and i-cycles for some i ∈ {5, 6, 7} is (3, 1)∗-choosable. In this paper,...

Some Erdős-Ko-Rado type extremal properties of families of vectors from {−1, 0, 1} are considered.

Author(s) Ayusawa, Ko; Yoshida, Eiichi; Imamura, Yumeko; Tanaka, Takayuki Citation Advanced Robotics, 30(8): 519-534 Issue Date 2016-04-18 Doc URL http://hdl.handle.net/2115/65110 Right This is an Accepted Manuscript of an article published by Taylor & Francis in Advanced Robotics on 18 April 2016, available online: http://www.tandfonline.com/10.1080/01691864.2016.1145596. Type article (author ...

1. Throughout this paper, c 1 , c2 , . . . denote absolute constants ; ko (a, fl, . . .), kr (a, f3, . . .), . . ., xo (a, /3, . . .), . . . denote constants depending only on the parameters a, /l, . . . ; v(n) denotes the number of the prime factors of the positive integer n, counted according to their multiplicity . The number of the elements of a finite set S is denoted by I S I . Let k, n b...

This paper investigates t-intersecting families of injections, where two injections a, b from [k] to [n] t-intersect if there exists X ⊆ [k] with |X| ≥ t such that a(x) = b(x) for all x ∈ X. We prove that if F is a 1-intersecting injection family of maximal size then all elements of F have a fixed image point in common. We show that when n is large in terms of k and t, the set of injections whi...