Recursive Schema Research Articles

Tutte polynomials for benzenoid systems with one branched hexagon

Benzenoid systems are natural graph representation of benzenoid hydrocarbons. Many chemically and combinatorially interesting indices and polynomials for bezenoid systems have been widely researched by both chemists and graph theorists. The Tutte polynomial of benzenoid chains without branched hexagons has already been computed by the recursive method. In this paper, by multiple recursion schema, an explicit expression for the Tutte polynomial of benzenoid systems with exactly one branched hexagon is obtained in terms of the number of hexagons on three linear or kinked chains. As a by-product, the number of spanning trees for these kind of benzenoid systems is determined.

Two function algebras defining functions in [formula omitted] boolean circuits

We describe the functions computed by boolean circuits in NCk by means of functions algebra for k≥1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic characterization of the complexity classes NCk for k≥1 without reference to a machine model, nor explicit bounds in the recursion schema. Actually, we give two equivalent descriptions of the classes NCk, k≥1. One is based on a tree structure à la Leivant, the other is based on words. This latter puts into light the role of computation of pointers in circuit complexity. We show that transducers are a key concept for pointer evaluation.

Type-based detection of XML query-update independence

This paper presents a novel static analysis technique to detect XML query-update independence, in the presence of a schema. Rather than types, our system infers chains of types. Each chain represents a path that can be traversed on a valid document during query/update evaluation. The resulting independence analysis is precise, although it raises a challenging issue: recursive schemas may lead to inference of infinitely many chains. A sound and complete approximation technique ensuring a finite analysis in any case is presented, together with an efficient implementation performing the chain-based analysis in polynomial space and time.

A Schema for Generating Relevant Logic Programming Semantics and its Applications in Argumentation Theory

In the literature, there are several approaches which try to perform common sense reasoning. Among them, the approaches which have probably received the most attention the last two decades are the approaches based on logic programming semantics with negation as failure and argumentation theory. Even though both approaches have their own features, it seems that they share some common behaviours which can be studied by considering the close relationship between logic programming semantics and extension-based argumentation semantics. In this paper, we will present a general recursive schema for defining new logic programming semantics. This schema takes as input any basic logic programming semantics, such as the stable model semantics, and gives as output a new logic programming semantics which satisfies some desired properties such as relevance and the existence of the intended models for every normal program. We will see that these new logic programming semantics can define candidate extension-based argumentation semantics. These new argumentation semantics will overcome some of the weakness of the extension-based argumentation semantics based on admissible sets. In fact, we will see that some of these new argumentation semantics have similar behaviour to the extension-based argumentation semantics built in terms of strongly connected components.

On tiered small jump operators

Predicative analysis of recursion schema is a method to characterize complexity classes like the class FPTIME of polynomial time computable functions. This analysis comes from the works of Bellantoni and Cook, and Leivant by data tiering. Here, we refine predicative analysis by using a ramified Ackermann's construction of a non-primitive recursive function. We obtain a hierarchy of functions which characterizes exactly functions, which are computed in O(n^k) time over register machine model of computation. For this, we introduce a strict ramification principle. Then, we show how to diagonalize in order to obtain an exponential function and to jump outside deterministic polynomial time. Lastly, we suggest a dependent typed lambda-calculus to represent this construction.

XML schema, tree logic and sheaves automata

XML documents may be roughly described as unranked, ordered trees and it is therefore natural to use tree automata to process or validate them. This idea has already been successfully applied in the context of Document Type Definition (DTD), the simplest standard for defining document validity, but additional work is needed to take into account XML Schema, a more advanced standard, for which regular tree automata are not satisfactory. In this paper, we introduce Sheaves Logic (SL), a new tree logic that extends the syntax of the – recursion-free fragment of – W3C XML Schema Definition Language (WXS). Then, we define a new class of automata for unranked trees that provides decision procedures for the basic questions about SL: model-checking; satisfiability; entailment. The same class of automata is also used to answer basic questions about WXS, including recursive schemas: decidability of type-checking documents; testing the emptiness of schemas; testing that a schema subsumes another one.

SCC-recursiveness: a general schema for argumentation semantics

In argumentation theory, Dung's abstract framework provides a unifying view of several alternative semantics based on the notion of extension. In this context, we propose a general recursive schema for argumentation semantics, based on decomposition along the strongly connected components of the argumentation framework. We introduce the fundamental notion of SCC-recursiveness and we show that all Dung's admissibility-based semantics are SCC-recursive, and therefore a special case of our schema. On these grounds, we argue that the concept of SCC-recursiveness plays a fundamental role in the study and definition of argumentation semantics. In particular, the space of SCC-recursive semantics provides an ideal basis for the investigation of new proposals: starting from the analysis of several examples where Dung's preferred semantics gives rise to questionable results, we introduce four novel SCC-recursive semantics, able to overcome the limitations of preferred semantics, while differing in other respects.

K-TSS language models in speech recognition systems

The aim of this work is to show the ability of stochastic regular grammars to generate accurate language models which can be well integrated, allocated and handled in a continuous speech recognition system. For this purpose, a syntactic version of the well-known n -gram model, called k -testable language in the strict sense (k -TSS), is used. The complete definition of a k -TSS stochastic finite state automaton is provided in the paper. One of the difficulties arising in representing a language model through a stochastic finite state network is that the recursive schema involved in the smoothing procedure must be adopted in the finite state formalism to achieve an efficient implementation of the backing-off mechanism. The use of the syntactic back-off smoothing technique applied to k -TSS language modelling allowed us to obtain a self-contained smoothed model integrating several k -TSS automata in a unique smoothed and integrated model, which is also fully defined in the paper. The proposed formulation leads to a very compact representation of the model parameters learned at training time: probability distribution and model structure. The dynamic expansion of the structure at decoding time allows an efficient integration in a continuous speech recognition system using a one-step decoding procedure. An experimental evaluation of the proposed formulation was carried out on two Spanish corpora. These experiments showed that regular grammars generate accurate language models (k -TSS) that can be efficiently represented and managed in real speech recognition systems, even for high values of k, leading to very good system performance.

On arithmetical first-order theories allowing encoding and decoding of lists

In Computer Science, n-tuples and lists are usual tools; we investigate both notions in the framework of first-order logic within the set of nonnegative integers. Gödel had firstly shown that the objects which can be defined by primitive recursion schema, can also be defined at first-order, using natural order and some coding devices for lists. Second he had proved that this encoding can be defined from addition and multiplication. We show this can be also done with addition and a weaker predicate, namely the coprimeness predicate. The theory of integers equipped with a pairing function can be decidable or not. The theory of decoding of lists (under some natural condition) is always undecidable. We distinguish the notions encoding of n-tuples and encoding of lists via some properties of decidability-undecidability. At last, we prove it is possible in some structure to encode lists although neither addition nor multiplication are definable in this structure.

Type-based derivational morphology

Approaches to morphology typically account for regular, completely productive affixation, while ignoring subregular and semiproductive schemata. The alternative approach to derivational morphology presented here relates exceptions and subregularities to productive rules. It accounts for the contribution lexicalized words make to the rule and for the fact that not all new formations follow the 'rules'. It also captures linguistically relevant generalizations that cannot be expressed in other theories. The approach is formalized in terms of complex recursive schemata structured in a multiple inheritance hierarchy, without positing lexical rules or lexical entries for affixes. These schemata structure the existing lexicon, reducing redundancy, and at the same time serve as the basis for productive word formation. The approach handles zero-derivation and other nonconcatenative morphology straightforwardly.

Synthesis of rewrite programs by higher-order and semantic unification

This paper presents a framework for synthesizing rewrite programs using higher-order and semantic unification. Many problems in computer science and artificial intelligence can be formalized as problems of higher-order unification. Among such problems is first-order anti-unification. In this paper, we show that first-order anti-unification can be regarded as a second-order matching problem and solved by the algorithm for higher-order unification. The problem of synthesizing a program from example input-output pairs can be considered as an extension of anti-unification because the problem of instantiating a program schema by examples consists of a pair of anti-unification problems. We show that higher-order unification can also be used to instantiate a recursive program schema and synthesize a rewrite program from examples. For expressing program schemata for rewrite programs, we extend lambda terms by introducing a construct called pseudo-abstraction. In order to synthesize a rewrite program that refers to existing ones as libraries, we merge higher-order unification and semantic unification because existing rewrite programs comprise a term rewriting system.

A generalization of mean value analysis to higher moments

Closed product-form queueing networks are considered. Recursive schemata are proposed for the higher moments of the number of customers in the queues, called “moment analysis”. As with mean value analysis (MVA), in general no state probabilities are needed. Approximation techniques for these schemata similar to those existing for MVA are introduced.

Decidable properties of monadic recursive schemas with a depth parameter

Monadic table counter schemas (MTCS) are defined as extensions of recursive monadic schemas by incorporating a depth-of-recursion counter. The family of languages generated by free MTCS under Herbrand interpretation is shown to be the family of ETOL languages. It is proven that the halting and divergence problems are decidable for free MTCS and that the freedom problem is decidable. Most of these results are obtained using results on regular control sequences from L system theory.

On the Unwinding of Flow-Charts with Stacks

Let A be a structure with the property that every flow-chart with one stack /every recursive schema/, total over A, is strongly equivalent in A to a loop-free schema. We show that every total flow-chart with one stack can be unwound in A.

Tree equivalence of linear recursive schemata is polynomial-time decidable

Tree equivalence of linear recursive schemata is polynomial-time decidable

Computational Complexity of Multiple Recursive Schemata

The computational complexity properties of a hierarchy of classes of subrecursive schemata are investigated. The schemata are derived from the multiple recursive operators of Peter. Concrete complexity measures based on specific computation rules and an underlying random-access stored-program machine (RASP) model are defined and the complexity properties induced by certain structural features are studied.It is shown to be undecidable whether two schemata have identical complexity. Upper bounds for the complexity of schemata are then given in terms of a hierarchy of multiple recursive function classes and lower bounds are given which demonstrate that multiple recursion is a thoroughly unfeasible computational tool in practice. Specifically, it is shown that a pure multiple recursive schema capable of defining nonprimitive recursive functions must have at least exponential complexity in terms of its arguments for all interpretations. We also show it undecidable whether a schema has the minimal complexity of...

Completeness results for the equivalence of recursive schemas

We investigate the possibilities of automating equivalence proofs for recursiveschemas. A formal proof system, adapted from work of J. W. deBakker and D. Scott, is shown to be complete with respect to provability of equivalence of pure recursive schemes. The result is obtained by showing the correspondence between operational and denotational semantics of a simple recursive language.