In this work we study the generation of singularities (shock waves) of the solution of the Cauchy problem for HamiltonJacobi equations in several space variables, under no assumption on convexity or concavity of the hamiltonian. We study the problem in the class of viscosity solutions, which are the correct class of weak solutions. We first examine the way the characteristics cross by identifyi...

Abstract—In this paper, we propose a chaotic complexvalued associative memory which can realize a dynamic association of multi-valued patterns. The proposed model is based on a complex-valued associative memory and a chaotic associative memory. The complex-valued associative memory can treat multi-valued patterns, and the chaotic associative memory can recall stored patterns dynamically. The pr...

Pattern Databases were a major breakthrough in heuristic search by solving hard combinatorial problems various orders of magnitude faster than state-of-the-art techniques at that time. Since then, they have received a lot of attention. Moreover, pattern databases are also researched in conjunction with other domain-independent techniques for solving planning tasks. However, they are not the onl...

1. Optimal transportation set up Let D, D∗ be two domains on Sn−1 or bounded domains in a manifold (D might be contained in one manifold and D∗ in another) with |∂D| = 0. LetN be a multi-valued mapping from D onto D∗ such thatN(x) is single-valued a.e. on D. For F ⊂ D∗, we set T (F) = N−1(F) = {x ∈ D : N(x) ∩ F , ∅}. We sayN is measurable if T (F) is Lebesgue measurable for any Borel set F ⊂ D∗...

In this paper, the minimization of incompletely specified multi-valued functions using functional decomposition is discussed. From the aspect of machine learning, learning samples can be implemented as minterms in multi-valued logic. The representation, can then be decomposed into smaller blocks, resulting in a reduced problem complexity. This gives induced descriptions through structuring, or ...

We define an invariant of a multi-valued logic gate by considering the number of certain threshold functions associated with the gate. We call this invariant the continuous sensitivity of the gate. We discuss a method for analysing continuous sensitivity of a multi-valued logic gate by using experimental data about the gate. In particular, we will show that this invariant provides a lower bound...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

In explicit state model checking of linear temporal logic properties, a Büchi automaton encodes a temporal property. It interleaves with a Kripke model to form a state space, which is searched for counterexamples. Multi-valued model checking considers additional truth values beyond the Boolean true and false; these values add extra information to the model, e.g. for the purpose of abstraction o...