We show how up-to techniques for (bi-)similarity can be used in the setting of weighted systems. The problems we consider are language equivalence, language inclusion and the threshold problem (also known as universality problem) for weighted automata. We build a bisimulation relation on the fly and work up-to congruence and up-to similarity. This requires to determine whether a pair of vectors...

Any instant of conscious perception is shaped by the differential contributions of all of our sensory organs. Complementary information in distinct sensory streams can be exploited by crossmodal integration. The principles that govern these integrative processes are not yet completely understood. The traditional bimodal nature of multisensory research hampers the exploration of the complex inte...

The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational congruence admitted by the stationary, axisymmetric spacetime. General precession formulae are obtained for circular orbits with arbitrary constant angular s...

Let S be a regular semigroup and C its lattice of congruences. We consider the sublattice Λ of C generated by σ-the least group, τ -the greatest idempotent pure, μ-the greatest idempotent separating and β-the least band congruence on S. To this end, we study the following special cases: (1) any three of these congruences generate a distributive lattice, (2) Λ is distributive, (3) the restrictio...

Let X35 be a Siegel cusp form of degree 2 and weight 35. Kikuta, Kodama and Nagaoka [4] proved that det T a(T, X35) ≡ 0 mod 23 for every half integral positive symmetric matrix T . In this paper, we give a finite number of examples of Hecke eigenforms of degree 2 and odd weights that have the same type of congruence relation above. We also introduce congruence relations for the Hecke eigenvalue...

In this paper we introduce a general class of lazy computation systems and deene a natural program equivalence for them. We prove that if an extensionality condition holds of each of the operators of a computation system, then the equivalence relation is a congruence, so that the usual kinds of equality reasoning are valid for it. This condition is a simple syntactic one, and is easy to verify ...

Let F = 〈F,R〉 be a finite Kripke frame. A congruence of F is a bisimulation of F that is also an equivalence relation on F. The set of all congruences of F is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that F is a finite linear frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through ...

Here we show that a notion of congruence in statistical structure across 2 0 frequency bands produces a useful definition of visual patterns for perceiving target distinctness. In order to reach such a conclusion, ,firstly, the notion of congruence is used to induce a representational model for 2 0 images. Secondly, the visual-pattern based representational model is used to define a visual targ...

The aim of this paper is to give a congruence on universal Bernoulli numbers which congruence is the same type of Kummer’s original paper [K]. The remakable thing is the index of prime power that is the modulus of the congruence is half of the original one. We mention in this paper that this estimate is best possible. It is suprising fact for the author that the critical index is not less than ...

Delaying the synchronisation of actions may reveal some hidden behaviour that would not happen if the synchronisation would meet the specified deadlines. This precise phenomenon makes bisimulation fail to be a congruence for the parallel composition of timed automata with deadlines, a variant of timed automata where time progress is controlled by deadlines imposed on each transition. This probl...