We investigate the valuedness of finite transducers in connection with their inner structure. We show: The valuedness of a finite-valued nondeterministic generalized sequential machine (NGSM) M with n states and output alphabet Δ is at most the maximum of (1-?1/#Δ?) · (2 k 1 · k 3 ) n · n n ·#Δ n 3 ·k 4 / 3 and ?1/#Δ?·(2 k 2 ·k 3 ·(1+k 4 )) n ·n n where k 1?6.25 and k 2?11.89 are constants and k 3?1 and k 4?0 are local structural parameters of M. There are two simple criteria which characterize the infinite valuedness of an NGSM. By these criteria, it is decidable in polynomial time whether or not an NGSM is infinite-valued. In both cases, #Δ > 1 and #Δ = 1, the above upper bound for the valuedness is almost optimal. By reduction, all results can be easily generalized to normalized finite transducers.

On the valuedness of finite transducers

Query answering algorithms on Xml streams check answer candidates on the fly in order to avoid the unnecessary buffering whenever possible. The delay and concurrency of a query are two measures for the degree of their streamability. They count the maximal number of stream elements during the life time for some query answer, and respectively, the maximal number of simultaneously alive answer candidates of a query. We study queries defined by deterministic nested word automata, which subsume large streamable fragments of XPath subject to schema restrictions by DTDs modulo P-time translations. We show that bounded and k-bounded delay and concurrency of such automata-defined queries are all decidable in polynomial time in the size of the automaton. Our results are obtained by P-time reduction to the bounded valuedness problem for recognizable relations between unranked trees, a problem that we show to be decidable in P-time.

https://hal.inria.fr/inria-00491495/document

Queries on Xml streams with bounded delay and concurrency

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with i¾?-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton Ain time $O(|A|_E^2)$, and finite or polynomial ambiguity in time $O(|A|_E^3)$, where |A| E denotes the number of transitions of A. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and based on a general algorithm for the composition or intersection of automata. We also give an algorithm to determine in time $O(|A|_E^3)$ the degree of polynomial ambiguity of a polynomially ambiguous automaton A. Finally, we present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton.

/pdf/general-algorithms-for-testing-the-ambiguity-of-finite-46bzl19z9y.pdf

General Algorithms for Testing the Ambiguity of Finite Automata

Earliest query answering is needed for streaming XML processing with optimal memory management. We study the feasibility of earliest query answering for node selection queries. Tractable queries are distinguished by a bounded number of concurrently alive answer candidates at every time point, and a bounded delay for node selection. We show that both properties are decidable in polynomial time for queries defined by deterministic automata for unranked trees. Our results are obtained by reduction to the bounded valuedness problem for recognizable relations between unranked trees.

/pdf/bounded-delay-and-concurrency-for-earliest-query-answering-265apbmiic.pdf

Bounded Delay and Concurrency for Earliest Query Answering

Automated Web Service Composition has gained a significant momentum in facilitating fast and efficient formation of business-to-business collaborations where an important objective is the utilization of existing services to respond to new business requirements in a timely manner. In this context, the service delegation problem can be formulated as follows: When a user poses a sequence of requests to a "service community", how to delegate the requests to the available services registered in the community so that the user requests are satisfied via a collaboration of these services. Here, we present a formal analysis of the constrained service delegation problem where users also provides a set of quality constraints about the delegation of their requests. We follow the "Roman" service composition framework and extend it with a QoS model. We use the Presburger arithmetic to specify constraints. We show that there exists a linear time algorithm for the service delegation problem. In fact, this algorithm is a finite memory algorithm that solves two variations of the service delegation problem by reading the activity sequence in two or multiple passes. We also show that these results are tight in the sense that the number of passes can't be further reduced. We also prove that the constrained service delegation problem can be solved in polynomial time in the number of service requests and delegation constraints.

A Weber

Papers

On the degree of ambuguity of finite automata