Displaying similar documents to “Coalgebras for Binary Methods: Properties of Bisimulations and Invariants”

The Helping Hierarchy

Patrizio Cintioli, Riccardo Silvestri (2010)

RAIRO - Theoretical Informatics and Applications

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Schöning [14] introduced a notion of helping and suggested the study of the class P help ( 𝒞 ) of the languages that can be helped by oracles in a given class 𝒞 . Later, Ko [12], in order to study the connections between helping and "witness searching" , introduced the notion of self-helping for languages. We extend this notion to classes of languages and show that there exists a self-helping class that we call SH which contains all the self-helping classes. We introduce the Helping hierarchy whose levels...

Threshold Circuits for Iterated Matrix Product and Powering

Carlo Mereghetti, Beatrice Palano (2010)

RAIRO - Theoretical Informatics and Applications

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The complexity of computing, via threshold circuits, the and of fixed-dimension k × k matrices with integer or rational entries is studied. We call these two problems 𝖨𝖬𝖯 𝗄 and 𝖬𝖯𝖮𝖶 𝗄 , respectively, for short. We prove that: (i) For k ≥ 2 , 𝖨𝖬𝖯 𝗄 does not belong to TC 0 , unless TC 0 = NC 1 .newline (ii) For : 𝖨𝖬𝖯 2 belongs to TC 0 while, for k ≥ 3 , 𝖨𝖬𝖯 𝗄 does not belong to TC 0 , unless TC 0 = NC 1 . (iii) For any , 𝖬𝖯𝖮𝖶 𝗄 belongs to TC 0 .

Entire solutions in ℝ 2 for a class of Allen-Cahn equations

Francesca Alessio, Piero Montecchiari (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a class of semilinear elliptic equations of the form 15.7cm - ε 2 Δ u ( x , y ) + a ( x ) W ' ( u ( x , y ) ) = 0 , ( x , y ) ∈ ℝ 2 where ε > 0 , a : ℝ → ℝ is a periodic, positive function and W : ℝ → ℝ is modeled on the classical two well Ginzburg-Landau potential W ( s ) = ( s 2 - 1 ) 2 . We look for solutions to ([see full textsee full text]) which verify the asymptotic conditions u ( x , y ) → ± 1 as x → ± ∞ uniformly with respect to y ∈ ℝ . We show variational methods that if is sufficiently small and is not constant, then ([see full textsee full text]) admits infinitely many of such solutions,...

Improved Lower Bounds on the Approximability of the Traveling Salesman Problem

Hans-Joachim Böckenhauer, Sebastian Seibert (2010)

RAIRO - Theoretical Informatics and Applications

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This paper deals with lower bounds on the approximability of different subproblems of the Traveling Salesman Problem (TSP) which is known not to admit any polynomial time approximation algorithm in general (unless 𝒫 = 𝒩𝒫 ). First of all, we present an improved lower bound for the Traveling Salesman Problem with Triangle Inequality, -TSP for short. Moreover our technique, an extension of the method of Engebretsen [11], also applies to the case of relaxed and sharpened triangle inequality, respectively,...