Relationships between different sets involving group and Drazin projectors and nonnegativity

This paper deals with nonnegativity of matrices and their group or Drazin inverses. Firstly, the nonnegativity of a square matrix A, its group inverse A# and its group projector AA# is used to define different sets for which relationships and characterizations are given. Next, an extension of the previous results for index greater than 1 is presented. Similar sets are introduced and studied for Drazin inverses and Drazin projectors considering the core-nilpotent decomposition. In addition, the results are applied to study the {l}-Drazin periodic matrices for l greater than or equal to 1.Herrero Debón, A.; Ramirez, FJ.; Thome, N. (2013). Relationships between different sets involving group and Drazin projectors and nonnegativity. Linear Algebra and its Applications. 438(4):1688-1699. doi:10.1016/J.LAA.2011.08.029S16881699438

A Declarative Semantics for CLP with Qualification and Proximity

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10

Methods for Proving Termination of Rewriting-based Programming Languages by Transformation

AbstractDespite the remarkable development of the theory of termination of rewriting, its application to high-level (rewriting-based) programming languages is far from being optimal. This is due to the need for features such as conditional equations and rules, types and subtypes, (possibly programmable) strategies for controlling the execution, matching modulo axioms, and so on, that are used in many programs and tend to place such programs outside the scope of current termination tools. The operational meaning of such features is often formalized in a proof theoretic manner by means of an inference system rather than just by a rewriting relation. The corresponding termination notions can also differ from the standard ones. During the last years we have introduced and implemented different notions and transformation techniques which have been proved useful for proving and disproving termination of such programs by using existing tools for proving termination of (variants of) rewriting. In this paper we provide an overview of our main contributions

Automatically Discovering Hidden Transformation Chaining Constraints

Model transformations operate on models conforming to precisely defined metamodels. Consequently, it often seems relatively easy to chain them: the output of a transformation may be given as input to a second one if metamodels match. However, this simple rule has some obvious limitations. For instance, a transformation may only use a subset of a metamodel. Therefore, chaining transformations appropriately requires more information. We present here an approach that automatically discovers more detailed information about actual chaining constraints by statically analyzing transformations. The objective is to provide developers who decide to chain transformations with more data on which to base their choices. This approach has been successfully applied to the case of a library of endogenous transformations. They all have the same source and target metamodel but have some hidden chaining constraints. In such a case, the simple metamodel matching rule given above does not provide any useful information

Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the calling contexts of the corresponding recursive function calls, it is possible to incorporate the forbidden pattern restrictions in the (adapted) notion of dependency pair chains, thus yielding a sound and complete approach to termination analysis. Building upon this contextual dependency pair framework we introduce a dependency pair processor that simplifies problems by analyzing the contextual information of the dependency pairs. Moreover, we show how this processor can be used to synthesize forbidden patterns suitable for a given term rewriting system on-the-fly during the termination analysis.Comment: In Proceedings IWS 2010, arXiv:1012.533

Comparing Tag Scheme Variations Using an Abstract Machine Generator

In this paper we study, in the context of a WAM-based abstract machine for Prolog, how variations in the encoding of type information in tagged words and in their associated basic operations impact performance and memory usage. We use a high-level language to specify encodings and the associated operations. An automatic generator constructs both the abstract machine using this encoding and the associated Prolog-to-byte code compiler. Annotations in this language make it possible to impose constraints on the final representation of tagged words, such as the effectively addressable space (fixing, for example, the word size of the target processor /architecture), the layout of the tag and value bits inside the tagged word, and how the basic operations are implemented. We evaluate large number of combinations of the different parameters in two scenarios: a) trying to obtain an optimal general-purpose abstract machine and b) automatically generating a specially-tuned abstract machine for a particular program. We conclude that we are able to automatically generate code featuring all the optimizations present in a hand-written, highly-optimized abstract machine and we canal so obtain emulators with larger addressable space and better performance

Graph generation to statically represent CSP processes

The CSP language allows the specification and verification of complex concurrent systems. Many analyses for CSP exist that have been successfully applied in different industrial projects. However, the cost of the analyses performed is usually very high, and sometimes prohibitive, due to the complexity imposed by the non-deterministic execution order of processes and to the restrictions imposed on this order by synchronizations. In this work, we define a data structure that allows us to statically simplify a specification before the analyses. This simplification can drastically reduce the time needed by many CSP analyses. We also introduce an algorithm able to automatically generate this data structure from a CSP specification. The algorithm has been proved correct and its implementation for the CSP's animator ProB is publicly available. © 2011 Springer-Verlag.This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación under grant TIN2008-06622-C03-02, by the Generalitat Valenciana under grant ACOMP/2010/042, and by the Universidad Politécnica de Valencia (Program PAID-06-08). Salvador Tamarit was partially supported by the Spanish MICINN under FPI grant BES-2009-015019.Llorens Agost, ML.; Oliver Villarroya, J.; Silva Galiana, JF.; Tamarit Muñoz, S. (2011). Graph generation to statically represent CSP processes. En Logic-Based Program Synthesis and Transformation. Springer Verlag (Germany). 6564:52-66. https://doi.org/10.1007/978-3-642-20551-4_4S52666564Brassel, B., Hanus, M., Huch, F., Vidal, G.: A Semantics for Tracing Declarative Multi-paradigm Programs. In: Moggi, E., Warren, D.S. (eds.) 6th ACM SIGPLAN Int’l Conf. on Principles and Practice of Declarative Programming (PPDP 2004), pp. 179–190. ACM, New York (2004)Butler, M., Leuschel, M.: Combining CSP and B for specification and property verification. In: Fitzgerald, J., Hayes, I.J., Tarlecki, A. (eds.) FM 2005. LNCS, vol. 3582, pp. 221–236. Springer, Heidelberg (2005)Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Upper Saddle River (1985)Kavi, K.M., Sheldon, F.T., Shirazi, B., Hurson, A.R.: Reliability Analysis of CSP Specifications using Petri Nets and Markov Processes. In: 28th Annual Hawaii Int’l Conf. on System Sciences (HICSS 1995). Software Technology, vol. 2, pp. 516–524. IEEE Computer Society, Washington, DC, USA (1995)Ladkin, P., Simons, B.: Static Deadlock Analysis for CSP-Type Communications. In: Responsive Computer Systems (Ch. 5). Kluwer Academic Publishers, Dordrecht (1995)Leuschel, M., Butler, M.: ProB: an Automated Analysis Toolset for the B Method. Journal of Software Tools for Technology Transfer 10(2), 185–203 (2008)Leuschel, M., Llorens, M., Oliver, J., Silva, J., Tamarit, S.: Static Slicing of CSP Specifications. In: Hanus, M. (ed.) 18th Int’l Symp. on Logic-Based Program Synthesis and Transformation (LOPSTR 2008), pp. 141–150. Technical report, DSIC-II/09/08, Universidad Politécnica de Valencia (July 2008)Leuschel, M., Llorens, M., Oliver, J., Silva, J., Tamarit, S.: SOC: a Slicer for CSP Specifications. In: Puebla, G., Vidal, G. (eds.) 2009 ACM SIGPLAN Symposium on Partial Evaluation and Semantics-based Program Manipulation (PEPM 2009), pp. 165–168. ACM, New York (2009)Leuschel, M., Llorens, M., Oliver, J., Silva, J., Tamarit, S.: The MEB and CEB static analysis for CSP specifications. In: Hanus, M. (ed.) LOPSTR 2008. LNCS, vol. 5438, pp. 103–118. Springer, Heidelberg (2009)Llorens, M., Oliver, J., Silva, J., Tamarit, S.: A Semantics to Generate the Context-sensitive Synchronized Control-Flow Graph (extended). Technical report DSIC, Universidad Politécnica de Valencia, Valencia, Spain (June 2010), http://www.dsic.upv.es/~jsilvaLlorens, M., Oliver, J., Silva, J., Tamarit, S.: Transforming Communicating Sequential Processes to Petri Nets. In: Topping, B.H.V., Adam, J.M., Pallarés, F.J., Bru, R., Romero, M.L. (eds.) Seventh Int’l Conference on Engineering Computational Technology (ICECT 2010). Civil-Comp Press, Stirlingshire, UK, Paper 26 (2010)Roscoe, A.W., Gardiner, P.H.B., Goldsmith, M., Hulance, J.R., Jackson, D.M., Scattergood, J.B.: Hierarchical Compression for Model-Checking CSP or How to Check 1020 Dining Philosophers for Deadlock. In: Brinksma, E., Cleaveland, R., Larsen, K.G., Margaria, T., Steffen, B. (eds.) TACAS 1995. LNCS, vol. 1019, pp. 133–152. Springer, Heidelberg (1995)Roscoe, A.W.: The Theory and Practice of Concurrency. Prentice Hall, Upper Saddle River (2005