We describe b-functions of linear free divisors and use these results to prove that the logarithmic comparison theorem holds for Koszul free reductive linear free divisors exactly if they are (strongly) Euler homogeneous.

This paper concerns linear context-free languages (LIN). We prove that LIN ⊆ NC (under UE∗−uniformity reduction). We introduce a new normal form for context-free grammars, called Dyck normal form. Using this new normal form we prove that for each context-free language L there exist an integer K and a homomorphism φ such that L = φ(D′ K), where D′ K ⊆ DK , and DK is the one-sided Dyck language o...

This work addresses the problem of offset-free Model Predictive Control (MPC) when tracking an asymptotically constant reference. In the first part, compact and intuitive conditions for offset-free MPC control are introduced by using the arguments of the internal model principle. In the second part, we study the case where the number of measured variables is larger than the number of tracked va...

We describe four different parsing algorithms for Linear Context-Free Rewriting Systems (Vijay-Shanker et al., 1987). The algorithms are described as deduction systems, and possible optimizations are discussed. The only parsing algorithms presented for linear contextfree rewriting systems (LCFRS; Vijay-Shanker et al., 1987) and the equivalent formalism multiple context-free grammar (MCFG; Seki ...

We consider the number of linear extensions of an N-free order P . We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The algorithm is polynomial if a new parameter called activity is bounded by a constant. The activity can be bounded in terms of parameters of the arc diagram....

The class of linear context-free rewriting systems has been introduced as a generalization of a class of grammar formalisms known as mildly context-sensitive. The recognition problem for linear context-free rewriting languages is studied at length here, presenting evidence that, even in some restricted cases, it cannot be solved efficiently. This entails the existence of a gap between, for exam...

Let S = k[x, ,..., x,] be a polynomial ring over a field and let A4 = @,*-a, M, be a finitely generated graded module; in the most interesting case A4 is an ideal of S. For a given natural number p, there is a great interest in the question: Can M be generated by (homogeneous) elements of degree <p? No simple answer, say in terms of the local cohomology of M, is known; but somewhat surprisingly...

We design algorithms for online linear optimization that have optimal regret and at the same time do not need to know any upper or lower bounds on the norm of the loss vectors. We achieve adaptiveness to norms of loss vectors by scale invariance, i.e., our algorithms make exactly the same decisions if the sequence of loss vectors is multiplied by any positive constant. Our algorithms work for a...

We define a transformation of models of additivefree propositional linear logic, closely related to de Paiva’s dialectica categories, but with a modified exponential based on Oliva’s dialectica interpretation of higher-order linear logic. As a result of this modification we obtain an elegant factorisation of dialectica models as linear-nonlinear adjunctions. From the point of view of game seman...