Modular Complexity Analysis for Term Rewriting

All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to their restricted power. To overcome this limitation the article introduces a modular framework which allows to infer (polynomial) upper bounds on the complexity of term rewrite systems by combining different criteria. Since the fundamental idea is based on relative rewriting, we study how matrix interpretations and match-bounds can be used and extended to measure complexity for relative rewriting, respectively. The modular framework is proved strictly more powerful than the conventional setting. Furthermore, the results have been implemented and experiments show significant gains in power.Comment: 33 pages; Special issue of RTA 201

Generic Encodings of Constructor Rewriting Systems

Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages, with the negation over patterns. We propose in this paper a concise and clear algorithm computing the difference over patterns which can be used to define generic encodings of constructor term rewriting systems with negation and order into classical term rewriting systems. As a direct consequence, established methods used for term rewriting systems can be applied to analyze properties of the extended systems. The approach can also be seen as a generic compiler which targets any language providing basic pattern matching primitives. The formalism provides also a new method for deciding if a set of patterns subsumes a given pattern and thus, for checking the presence of useless patterns or the completeness of a set of patterns.Comment: Added appendix with proofs and extended example

Generic Encodings of Constructor Rewriting Systems

International audienceRewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages, with the negation over patterns. We propose in this paper a concise and clear algorithm computing the difference over patterns which can be used to define generic encodings of constructor term rewriting systems with negation and order into classical term rewriting systems. As a direct consequence, established methods used for term rewriting systems can be applied to analyze properties of the extended systems. The approach can also be seen as a generic compiler which targets any language providing basic pattern matching primitives. The formalism provides also a new method for deciding if a set of patterns subsumes a given pattern and thus, for checking the presence of useless patterns or the completeness of a set of patterns

Diversity, stability, and evolvability in models of early evolution

Based on the RNA world hypothesis, we outline a possible evolutionary route from infrabiological systems to early protocells. To assess the scientific merits of the different models of prebiotic evolution and to suggest directions for future research, we investigate the diversity-maintaining ability, evolutionary/ecological stability, and evolvability criteria of existing RNA world model systems for the origin of life. We conclude that neither of the studied systems satisfies all of the aforementioned criteria, although some of them are more convincing than the others. Furthermore, we found that the most conspicuous features of the proposed prebiotic evolutionary scenarios are their increasing spatial inhomogeneity along with increasing plasticity, evolvability, and functional diversity. All of these characteristics change abruptly with the emergence of the protocells

Modular Complexity Analysis for Term Rewriting

All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to their restricted power. To overcome this limitation the article introduces a modular framework which allows to infer (polynomial) upper bounds on the complexity of term rewrite systems by combining different criteria. Since the fundamental idea is based on relative rewriting, we study how matrix interpretations and match-bounds can be used and extended to measure complexity for relative rewriting, respectively. The modular framework is proved strictly more powerful than the conventional setting. Furthermore, the results have been implemented and experiments show significant gains in power

Modular complexity analysis via relative complexity

Abstract. In this paper we introduce a modular framework which allows to infer (feasible) upper bounds on the (derivational) complexity of term rewrite systems by combining different criteria. All current investigations to analyze the derivational complexity are based on a single termination proof, possibly preceded by transformations. We prove that the modular framework is strictly more powerful than the conventional setting. Furthermore, the results have been implemented and experiments show significant gains in power. 1

Proving Termination of Rewrite Systems using Bounds

Abstract. The use of automata techniques to prove the termination of string rewrite systems and left-linear term rewrite systems is advocated by Geser et al. in a recent sequence of papers. We extend their work to non-left-linear rewrite systems. The key to this extension is the introduction of so-called raise rules and the use of tree automata that are not quite deterministic. Furthermore, we present negative solutions to two open problems related to string rewrite systems.

On Implementing Modular Complexity Analysis

We recall the recent approach by (Zankl and Korp, 2010) to prove upper bounds on the (derivational) complexity of term rewrite systems modularly. In this note we show that this approach is suitable to tighten bounds after they have been established. The idea is to replace proof steps with a large bound by (new) proofs that yield smaller bounds. An evaluation of the approach shows the benefits.

Minor cognitive disturbances in X-linked spinal and bulbar muscular atrophy, Kennedy's disease

Kasper E, Wegrzyn M, Marx I, et al. Minor cognitive disturbances in X-linked spinal and bulbar muscular atrophy, Kennedy's disease. Amyotrophic Lateral Sclerosis and Frontotemporal Degeneration. 2014;15(1-2):15-20.Spinal and bulbar muscular atrophy (SBMA), Kennedy's disease, is an adult-onset hereditary neurodegenerative disorder, associated predominantly with a lower motor neuron syndrome and eventually endocrine and sensory disturbances. In contrast to other motor neuron diseases such as amyotrophic lateral sclerosis (ALS), the impairment of cognition in SBMA is not well documented. We conducted a systematic cross-sectional neuropsychological study in order to investigate cognition in SBMA patients more thoroughly. We investigated 20 genetically proven SBMA patients compared to 20 age-and education-matched control subjects using a comprehensive neuropsychological test battery, measuring executive functioning, attention, memory and visuospatial abilities. The SBMA patients performed significantly worse than healthy controls in three sub-tests in the executive and attention domains. This low performance was in the working memory (digit span backward task), verbal fluency category (single letter fluency task) and memory storage capacity (digit span forward task). No disturbances were detected in other cognitive domains. The impairments were subclinical and not relevant to the patients ' everyday functioning. In addition, no correlations were found between cognitive scores and the CAG repeat length. In conclusion, we found minor cognitive disturbances in patients with SBMA, which could indicate subtle frontal lobe dysfunction. These findings extend our neurobiological understanding of SBMA