Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...

For functions defined on Cn or Rn+ we construct a dequantization transform f 7→ f̂ ; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂f̂ of f̂ coincides with the Newton polytope of f . For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempotent semirin...

For functions defined on C or R+ we construct a dequantization transform f 7→ f̂ ; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂f̂ of f̂ at the origin coincides with the Newton polytope of f . For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempo...

In this paper we introduce a novel use of the lexicographic semiring and motivate its use for speech and language processing tasks. We prove that the semiring allows for exact encoding of backoff models with epsilon transitions. This allows for off-line optimization of exact models represented as large weighted finite-state transducers in contrast to implicit (on-line) failure transition repres...

Soft constraints are recognised as being important for many constraints applications. These include (a) over-constrained problems, where we cannot satisfy all the constraints, (b) situations where a constraint can be partially satisfied, so that there are degrees of satisfaction, and (c) where the identity of a constraint is uncertain, so that it can be uncertain whether a constraint is satisfi...

The novel contribution of this work is the construction of anytime algorithms in a generic framework, which automatically gives us instantiations in many useful domains. We also show that semiring induced valuation algebras, an important subclass of valuation algebras are amenable to anytime inference. Anytime inference, and inference algorithms in general have been a well-researched area in th...

We introduce two generalizations of synchronizability to automata with transitions weighted in an arbitrary semiring K = (K,+, ·,0,1). For states p,q and word u, let (pu)q ∈ K denote the sum of the weights of all u-labeled paths from p to q, with the weigth of a path being the product of the weights of its edges, as usual. We call the automaton A location-synchronizable if ∃q,u: ∀p,r (pu)r 6= 0...

Previous work on context-specific independence in Bayesian networks is driven by a common goal, namely to represent the conditional probability tables in a most compact way. In this paper, we argue from the view point of the knowledge compilation map and conclude that the language of Ordered Binary Decision Diagrams (OBDD) is the most suitable one for representing probability tables, in additio...

Fixed point equations x = F (x) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Equations over the semiring of the real numbers can be solved numerically using Newton’s method. We generalize the method to any ω-continuous semiring and show that it converges faster to the least fixed point than the Kleene sequence 0, F (0), F (F (0)), . . . ...