Variant-Based Satisfiability

Although different satisfiability decision procedures can be combined by algorithms such as those of Nelson-Oppen or Shostak, current tools typically can only support a finite number of theories to use in such combinations. To make SMT solving more widely applicable, generic satisfiability algorithms that can allow a potentially infinite number of decidable theories to be user-definable, instead of needing to be built in by the implementers, are highly desirable. This work studies how folding variant narrowing, a generic unification algorithm that offers good extensibility in unification theory, can be extended to a generic variant-based satisfiability algorithm for the initial algebras of its user-specified input theories when such theories satisfy Comon-Delaune's finite variant property (FVP) and some extra conditions. Several, increasingly larger infinite classes of theories whose initial algebras enjoy decidable variant-based satisfiability are identified, and a method based on descent maps to bring other theories into these classes and to improve the generic algorithm's efficiency is proposed and illustrated with examples.Partially supported by NSF Grant CNS 13-19109.Ope

Normal forms and normal theories in conditional rewriting

this is the author’s version of a work that was accepted for publication in Journal of Logical and Algebraic Methods in Programming. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Logical and Algebraic Methods in Programming vol. 85 (2016) DOI 10.1016/j.jlamp.2015.06.001We present several new concepts and results on conditional term rewriting within the general framework of order-sorted rewrite theories (OSRTs), which support types, subtypes and rewriting modulo axioms, and contains the more restricted framework of conditional term rewriting systems (CTRSs) as a special case. The concepts shed light on several subtle issues about conditional rewriting and conditional termination. We point out that the notions of irreducible term and of normal form, which coincide for unconditional rewriting, have been conflated for conditional rewriting but are in fact totally different notions. Normal form is a stronger concept. We call any rewrite theory where all irreducible terms are normal forms a normal theory. We argue that normality is essential to have good executability and computability properties. Therefore we call all other theories abnormal, freaks of nature to be avoided. The distinction between irreducible terms and normal forms helps in clarifying various notions of strong and weak termination. We show that abnormal theories can be terminating in various, equally abnormal ways; and argue that any computationally meaningful notion of strong or weak conditional termination should be a property of normal theories. In particular we define the notion of a weakly operationally terminating (or weakly normalizing) OSRT, discuss several evaluation mechanisms to compute normal forms in such theories, and investigate general conditions under which the rewriting-based operational semantics and the initial algebra semantics of a confluent, weakly normalizing OSRT coincide thanks to a notion of canonical term algebra. Finally, we investigate appropriate conditions and proof methods to ensure that a rewrite theory is normal; and characterize the stronger property of a rewrite theory being operationally terminating in terms of a natural generalization of the notion of quasidecreasing order. (C) 2015 Elsevier Inc. All rights reserved.We thank the anonymous referees for their constructive criticism and helpful comments. This work has been partially supported by NSF grant CNS 13-19109. Salvador Lucas' research was developed during a sabbatical year at UIUC and was also supported by the EU (FEDER), Spanish MINECO projects TIN2010-21062-C02-02 and TIN 2013-45732-C4-1-P, and GV grant BEST/2014/026 and project PROMETEO/2011/052.Lucas Alba, S.; Meseguer, J. (2016). Normal forms and normal theories in conditional rewriting. Journal of Logical and Algebraic Methods in Programming. 85(1):67-97. https://doi.org/10.1016/j.jlamp.2015.06.001S679785

Generalized Rewrite Theories, Coherence Completion and Symbolic Methods

A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those for standard rewrite theories, including a generalized notion of coherence, are given. Symbolic executability, including coherence, is both ensured and made available for a wide class of such theories by automatable theory transformations. Using these foundations, several symbolic reasoning methods using generalized rewrite theories are studied, including: (i) symbolic description of sets of terms by pattern predicates; (ii) reasoning about universal reachability properties by generalized rewriting; (iii) reasoning about existential reachability properties by constrained narrowing; and (iv) symbolic verification of safety properties such as invariants and stability properties.This work has been partially supported by NRL under contract number N00173-17-1-G002.Ope

Formal Design of Cloud Computing Systems in Maude

Cloud computing systems are complex distributed systems whose design is challenging for two main reasons: (1) since they are distributed systems, a correct design is very hard to achieve by testing alone; and (2) cloud computing applications have high availability and performance requirements; but these are hard to measure before implementation and hard to compare between different implementations. This paper summarizes our experience in using formal specification in Maude and model checking analysis to quickly explore the design space of a cloud computing system to achieve a high quality design that: (1) has verified correctness guarantees; (2) has better performance properties than other design alternatives so explored; (3) can be achieved before an actual implementation; and (4) can be used for both rapid prototyping and for automatic code generation.Ope

Order-Sorted Equality Enrichments Modulo Axioms

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for checking key properties such as confluence, termination, and sufficient completeness. Such specifications would instead be amenable to formal analysis if an equationally-defined equality predicate enriching the algebraic data types were to be added to them. Furthermore, having an equationally-defined equality predicate is very useful in its own right, particularly in inductive theorem proving. Is it possible to effectively define a theory transformation epsilon bar right arrow epsilon(similar to) that extends an algebraic specification epsilon to a specification epsilon(similar to) having an equationally-defined equality predicate? This paper answers this question in the affirmative for a broad class of order-sorted conditional specifications epsilon that are sort-decreasing, ground confluent, and operationally terminating modulo axioms B and have a subsignature of constructors. The axioms B can consist of associativity, or commutativity, or associativity-commutativity axioms, so that the constructors are free modulo B. We prove that the transformation epsilon bar right arrow epsilon(similar to) preserves all the just-mentioned properties of epsilon. The transformation has been automated in Maude using reflection and is used as a component in many Maude formal tools. (C) 2014 Elsevier B.V. All rights reserved.This work has been supported in part by NSF Grants CCF 09-05584 and CNS 13-19109, the EU (FEDER) and the Spanish MINECO under Grants TIN 2010-21062-C02 and TIN 2013-45732-C4-1-P, and by the Generalitat Valenciana, ref. PROMETEO/2011/052. Raul Gutierrez is also partially supported by a Juan de la Cierva Fellowship from the Spanish MINECO, ref. JCI-2012-13528.Gutiérrez Gil, R.; Meseguer, J.; Rocha, C. (2015). Order-Sorted Equality Enrichments Modulo Axioms. Science of Computer Programming. 99:235-261. https://doi.org/10.1016/j.scico.2014.07.003S2352619

Rewriting Modulo SMT

Combining symbolic techniques such as: (i) SMT solving, (ii) rewriting modulo theories, and (iii) model checking can enable the analysis of infinite-state systems outside the scope of each such technique. This paper proposes rewriting modulo SMT as a new technique combining the powers of (i)-(iii) and ideally suited to model and analyze infinite-state open systems; that is, systems that interact with a non-deterministic environment. Such systems exhibit both internal non-determinism due to the system, and external non-determinism due to the environment. They are not amenable to finite-state model checking analysis because they typically are infinite-state. By being reducible to standard rewriting using reflective techniques, rewriting modulo SMT can both naturally model and analyze open systems without requiring any changes to rewriting-based reachability analysis techniques for closed systems. This is illustrated by the analysis of a real-time system beyond the scope of timed automata methods

Investigating the protective properties of dimethyl fumarate and Nrf2 signalling in response to drug toxicity

Liver disease represents a major cause of mortality and morbidity. Despite the regenerative capacity of the liver, maintained injury or acute injury can lead to loss of liver function and disease. The most common cause of acute liver damage is drug-induced liver injury (DILI). This can lead to organ failure and possible death. Therefore, new therapies to reduce the severity of the injury are required. Stimulation of anti-inflammatory and anti-oxidative stress pathways during the resolution of the injury have been proposed as powerful approaches to reduce organ injury and to enhance regeneration. A main transcription factor which regulates anti-inflammatory and anti-oxidative stress is ‘nuclear factor erythroid-derived 2-like 2’ (Nrf2). Therefore, pharmacological activation of the Nrf2 pathway offers the potential to exert a cytoprotective effect promoting tissue regeneration. Dimethyl fumarate (DMF) is a drug approved for some forms of multiple sclerosis. DMF’s protection is due in part by activation of the Nrf2 pathway. We hypothesize that DMF could be used to reduce the severity of DILI via Nrf2 activation. This thesis explores the protective effects of DMF and Nrf2 signalling during paracetamol-induced hepatotoxicity using in vitro and in vivo models. For the in vitro studies, a semi-automated platform to produce hepatocytes-like cells (HLCs) from human pluripotent stem cells was employed. Single-cell high content image analysis was performed to understand Nrf2 nuclear translocation dynamics following DMF administration. The protective properties of DMF were tested in three different combinations: pre-treatment prior to paracetamol incubation, co-treatment or post-treatment following paracetamol injury. In all cases, DMF protected HLCs from paracetamol exposure. These findings were validated in a Zebrafish model of paracetamol injury. A zebrafish liver GFP reporter line was employed to detect fluorescence changes upon paracetamol exposure. Pre-treatment with DMF prior to paracetamol injury reduced the level of GFP loss. RNA sequencing from both models identified that DMF protection was mediated via Nrf2 pathway stimulation. This was mainly by an increase in cell metabolism and oxidative stress management as well as reducing pro-inflammatory pathways activation. In summary, the findings of this work provide new understanding on the effects of DMF in the modulation of the Nrf2 pathway during paracetamol-induced liver injury. These studies may provide a platform to develop new treatment regimes for patients with acute liver disease

The Evolution Of Disability Among Surveys In Spain

The definition of the word disability is controversial, due to his complexity and multidimensionality. The successive disability models and their empirical measurement in the diverse health national surveys vary greatly. The International Classification of Functioning, Disability, and Health (World Health Organization, 2001), known as the ICF, sees disability as the outcome of interactions between the features of the individual and the physical, social, and attitudinal world. This approach has the dual advantage of stressing the social context in which individuals are enabled or excluded while not ruling out the roles of bodies and medicine. In this paper, we analyze the evolution of the measurement of disability among three health national surveys in Spain

Are Spanish Health Services Appropriate To The Needs Of People With Disabilities?

In recent decades, social policies have advanced greatly in developed countries, especially with regard to disabilities. This has led to greater resources for these social policies, especially those related to health care. However, people with disabilities have different needs, which are not always reflected in health service care. So, using data of the 2006 Spanish National Health Survey (ENSE 2006), this study focuses on this group of people and analyses the main causes for which they do not receive the health care required. It also examines their healthy behaviour habits, highlighting possible differences with the entire population. This information should be considered when providing health and social care services to people with disabilities