On the determinant of quaternionic polynomial matrices and its application to system stability

In this paper, we propose a definition of determinant for quaternionic, polynomial matrices inspired by the well-known Dieudonne determinant for the constant case. This notion allows to characterize the stability of linear dynamical systems with quaternionic coefficients, yielding results which generalize the ones obtained for the real and complex cases

Stability of quaternionic systems: a determinantal approach

In this paper we propose a definition of determinant for quaternionic polynomial matrices. This definition is later used in the study of stability of linear quaternionic systems within the behavioral setting

Towards Multi-Threaded Local Tabling Using a Common Table Space

Multi-threading is currently supported by several well-known Prolog systems providing a highly portable solution for applications that can benefit from concurrency. When multi-threading is combined with tabling, we can exploit the power of higher procedural control and declarative semantics. However, despite the availability of both threads and tabling in some Prolog systems, the implementation of these two features implies complex ties to each other and to the underlying engine. Until now, XSB was the only Prolog system combining multi-threading with tabling. In XSB, tables may be either private or shared between threads. While thread-private tables are easier to implement, shared tables have all the associated issues of locking, synchronization and potential deadlocks. In this paper, we propose an alternative view to XSB's approach. In our proposal, each thread views its tables as private but, at the engine level, we use a common table space where tables are shared among all threads. We present three designs for our common table space approach: No-Sharing (NS) (similar to XSB's private tables), Subgoal-Sharing (SS) and Full-Sharing (FS). The primary goal of this work was to reduce the memory usage for the table space but, our experimental results, using the YapTab tabling system with a local evaluation strategy, show that we can also achieve significant reductions on running time.Comment: To appear in Theory and Practice of Logic Programmin

Global reachability of 2D structured systems

In this paper the new concept of 2D structured system is defined and a characterization of global reachability is obtained. This extends a well known result for 1D structured systems, according to which (A ,B ) is (generically) reachable if and only if the matrix [A B] is full generically row rank and irreducible

Periodic orbits 1-5 of quadratic polynomials on a new coordinate plane

While iterating the quadratic polynomial f_{c}(x)=x^{2}+c the degree of the iterates grows very rapidly, and therefore solving the equations corresponding to periodic orbits becomes very difficult even for periodic orbits with a low period. In this work we present a new iteration model by introducing a change of variables into an (u,v)-plane, which changes situation drastically. As an excellent example of this we can compare equations of orbits period four on (x,c)- and (u,v)-planes. In the latter case, this equation is of degree two with respect to u and it can be solved explicitly. In former case the corresponding equation ((((x^{2}+c)^{2}+c)^{2}+c)^{2}+c-x)/((x^{2}+c)^{2}+c-x)=0 is of degree 12 and it is thus much more difficult to solve

Efficient Instance Retrieval of Subgoals for Subsumptive Tabled Evaluation of Logic Programs

Tabled evaluation is an implementation technique that solves some problems of traditional Prolog systems in dealing with recursion and redundant computations. Most tabling engines determine if a tabled subgoal will produce or consume answers by using variant checks. A more refined method, named call subsumption, considers that a subgoal A will consume from a subgoal B if A is subsumed by (an instance of) B, thus allowing greater answer reuse. We recently developed an extension, called Retroactive Call Subsumption, that improves upon call subsumption by supporting bidirectional sharing of answers between subsumed/subsuming subgoals. In this paper, we present both an algorithm and an extension to the table space data structures to efficiently implement instance retrieval of subgoals for subsumptive tabled evaluation of logic programs. Experiments results using the YapTab tabling system show that our implementation performs quite well on some complex benchmarks and is robust enough to handle a large number of subgoals without performance degradation.Comment: Theory and Practice of Logic Programming, 27th Int'l. Conference on Logic Programming (ICLP 2011) Special Issue, volume 11, issue 4-

Or-Parallel Prolog Execution on Clusters of Multicores

Logic Programming languages, such as Prolog, provide an excellent framework for the parallel execution of logic programs. In particular, the inherent non-determinism in the way logic programs are structured makes Prolog very attractive for the exploitation of implicit parallelism. One of the most noticeable sources of implicit parallelism in Prolog programs is or-parallelism. Or-parallelism arises from the simultaneous evaluation of a subgoal call against the clauses that match that call. Arguably, the most successful model for or-parallelism is environment copying, that has been efficiently used in the implementation of or-parallel Prolog systems both on shared memory and distributed memory architectures. Nowadays, multicores and clusters of multicores are becoming the norm and, although, many parallel Prolog systems have been developed in the past, to the best of our knowledge, none of them was specially designed to explore the combination of shared with distributed memory architectures. Motivated by our past experience, in designing and developing parallel Prolog systems based on environment copying, we propose a novel computational model to efficiently exploit implicit parallelism from large scale real-world applications specialized for the novel architectures based on clusters of multicores