Rewriting Modulo SMT and Open System Analysis

Rewriting modulo SMT is a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. In this talk, I will be discussing the main conceptual and technical ideas behind rewriting modulo SMT, its state of implementation in the Maude system, and some research challenges to be tackled during the next few years.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Rewriting Modulo SMT and Open System Analysis

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.NSF Grant CNS 13-19109 and NASA Research Cooperative Agreement No. NNL09AA00AOpe

Using Overlapping Communities and Network Structure for Identifying Reduced Groups of Stress Responsive Genes

This paper proposes a workflow to identify genes responding to a specific treatment in an organism, such as abiotic stresses, a main cause of extensive agricultural production losses worldwide. On input RNA sequencing read counts (measured for genotypes under control and treatment conditions) and biological replicates, it outputs a collection of characterized genes, potentially relevant to treatment. Technically, the proposed approach is both a generalization and an extension of WGCNA; its main goal is to identify specific modules in a network of genes after a sequence of normalization and filtering steps. In this work, module detection is achieved by using Hierarchical Link Clustering, which can recognize overlapping communities and thus have more biological meaning given the overlapping regulatory domains of systems that generate co-expression. Additional steps and information are also added to the workflow, where some networks in the intermediate steps are forced to be scale-free and LASSO regression is employed to select the most significant modules of phenotypical responses to stress. Finally, the workflow is showcased with a systematic study on rice (Oryza sativa), a major food source that is known to be highly sensitive to salt stress: a total of 6 modules are detected as relevant in the response to salt stress in rice; these genes may act as potential targets for the improvement of salinity tolerance in rice cultivars. The proposed workflow has the potential to ultimately reduce the search-space for candidate genes responding to a specific treatment, which can considerably optimize the effort, time, and money invested by researchers in the experimental validation of stress responsive genes

Automatic proof-search heuristics in the maude invariant analyzer tool

The Invariant Analyzer Tool is an interactive tool that mechanizes an inference system for proving safety properties of concurrent systems, which may be infinite-state or whose set of initial states may be infinite. This paper presents the automatic proof-search heuristics at the core of the Maude Invariant Analyzer Tool, which provide a substantial degree of automation and can automatically discharge many proof obligations without user intervention. These heuristics can take advantage of equationally defined equality predicates and include rewriting, narrowing, and SMT-based proof-search techniques

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