Constrained narrowing for conditional equational theories modulo axioms

For an unconditional equational theory (Sigma, E) whose oriented equations (E) over arrow are confluent and terminating, narrowing provides an E-unification algorithm. This has been generalized by various authors in two directions: (i) by considering unconditional equational theories (Sigma, E boolean OR B) where the (E) over arrow are confluent, terminating and coherent modulo axioms B, and (ii) by considering conditional equational theories. Narrowing for a conditional theory (Sigma, E boolean OR B) has also been studied, but much less and with various restrictions. In this paper we extend these prior results by allowing conditional equations with extra variables in their conditions, provided the corresponding rewrite rules (E) over arrow are confluent, strictly coherent, operationally terminating modulo B and satisfy a natural determinism condition allowing incremental computation of matching substitutions for their extra variables. We also generalize the type structure of the types and operations in Sigma to be order-sorted. The narrowing method we propose, called constrained narrowing, treats conditions as constraints whose solution is postponed. This can greatly reduce the search space of narrowing and allows notions such as constrained variant and constrained unifier that can cover symbolically possibly infinite sets of actual variants and unifiers. It also supports a hierarchical method of solving constraints. We give an inference system for hierarchical constrained narrowing modulo B and prove its soundness and completeness. (C) 2015 Elsevier B.V. All rights reserved.We thank the anonymous referees for their constructive criticism and their very detailed and helpful suggestions for improving an earlier version of this work. We also thank Luis Aguirre for kindly giving us additional suggestions to improve the text. This work has been partially supported by NSF Grant CNS 13-19109 and by the EU (FEDER) and the Spanish MINECO under grant TIN 2013-45732-C4-1-P, and by Generalitat Valenciana PROMETEOII/2015/013.Cholewa, A.; Escobar Román, S.; Meseguer, J. (2015). Constrained narrowing for conditional equational theories modulo axioms. Science of Computer Programming. 112:24-57. https://doi.org/10.1016/j.scico.2015.06.001S245711

Advanced Features in Protocol Verification: Theory, Properties, and Efficiency in Maude-NPA

The area of formal analysis of cryptographic protocols has been an active one since the mid 80’s. The idea is to verify communication protocols that use encryption to guarantee secrecy and that use authentication of data to ensure security. Formal methods are used in protocol analysis to provide formal proofs of security, and to uncover bugs and security flaws that in some cases had remained unknown long after the original protocol publication, such as the case of the well known Needham-Schroeder Public Key (NSPK) protocol. In this thesis we tackle problems regarding the three main pillars of protocol verification: modelling capabilities, verifiable properties, and efficiency. This thesis is devoted to investigate advanced features in the analysis of cryptographic protocols tailored to the Maude-NPA tool. This tool is a model-checker for cryptographic protocol analysis that allows for the incorporation of different equational theories and operates in the unbounded session model without the use of data or control abstraction. An important contribution of this thesis is relative to theoretical aspects of protocol verification in Maude-NPA. First, we define a forwards operational semantics, using rewriting logic as the theoretical framework and the Maude programming language as tool support. This is the first time that a forwards rewriting-based semantics is given for Maude-NPA. Second, we also study the problem that arises in cryptographic protocol analysis when it is necessary to guarantee that certain terms generated during a state exploration are in normal form with respect to the protocol equational theory. We also study techniques to extend Maude-NPA capabilities to support the verification of a wider class of protocols and security properties. First, we present a framework to specify and verify sequential protocol compositions in which one or more child protocols make use of information obtained from running a parent protocol. Second, we present a theoretical framework to specify and verify protocol indistinguishability in Maude-NPA. This kind of properties aim to verify that an attacker cannot distinguish between two versions of a protocol: for example, one using one secret and one using another, as it happens in electronic voting protocols. Finally, this thesis contributes to improve the efficiency of protocol verification in Maude-NPA. We define several techniques which drastically reduce the state space, and can often yield a finite state space, so that whether the desired security property holds or not can in fact be decided automatically, in spite of the general undecidability of such problems.Santiago Pinazo, S. (2015). Advanced Features in Protocol Verification: Theory, Properties, and Efficiency in Maude-NPA [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/4852

An Efficient Canonical Narrowing Implementation with Irreducibility and SMT Constraints for Generic Symbolic Protocol Analysis

Narrowing and unification are very useful tools for symbolic analysis of rewrite theories, and thus for any model that can be specified in that way. A very clear example of their application is the field of formal cryptographic protocol analysis, which is why narrowing and unification are used in tools such as Maude-NPA, Tamarin and Akiss. In this work we present the implementation of a canonical narrowing algorithm, which improves the standard narrowing algorithm, extended to be able to process rewrite theories with conditional rules. The conditions of the rules will contain SMT constraints, which will be carried throughout the execution of the algorithm to determine if the solutions have associated satisfiable or unsatisfiable constraints, and in the latter case, discard them.Comment: 41 pages, 7 tables, 1 algorithm, 9 example

A Reduced Semantics for Deciding Trace Equivalence

Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e., without replication) by means of symbolic execution and constraint solving. However, this does not suffice to obtain practical tools. Current prototypes suffer from a classical combinatorial explosion problem caused by the exploration of many interleavings in the behaviour of processes. M\"odersheim et al. have tackled this problem for reachability properties using partial order reduction techniques. We revisit their work, generalize it and adapt it for equivalence checking. We obtain an optimisation in the form of a reduced symbolic semantics that eliminates redundant interleavings on the fly. The obtained partial order reduction technique has been integrated in a tool called APTE. We conducted complete benchmarks showing dramatic improvements.Comment: Accepted for publication in LMC

Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems

The role of anxiety in perceiving and realizing affordances

Three experiments were conducted to examine the role of anxiety in perceiving and realizing affordances in wall climbing. Identical traverses were situated high and low on a climbing wall to manipulate anxiety. In Experiment 1, participants judged their maximal overhead reachability and performed maximal reaches on the climbing wall. Anxiety was found to reduce both perceived and actual maximal reaching height. In Experiment 2, participants climbed from right to left and back again on the high and low traverses, which now entailed an abundance of holds. Consistent with the reduction of perceived and actual maximal reaching height found in Experiment 1, anxiety led to the use of more holds. Finally, in Experiment 3, points of light were sequentially projected around the participants while they were climbing to measure attention. As participants detected fewer lights in the high-anxiety condition, it was concluded that anxiety narrowed attention. In general, the results underscored that the actor's emotional state plays an important role in perceiving and realizing affordances and that the perception of affordances changes as the accompanying action capabilities change. Copyright © 2006, Lawrence Krlbaum Associates, Inc

A Partial Evaluation Framework for Order-sorted Equational Programs modulo Axioms

[EN] Partial evaluation is a powerful and general program optimization technique with many successful applications. Existing PE schemes do not apply to expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF, and ELAN, which support: 1) rich type structures with sorts, subsorts, and overloading; and 2) equational rewriting modulo various combinations of axioms such as associativity, commutativity, and identity. In this paper, we develop the new foundations needed and illustrate the key concepts by showing how they apply to partial evaluation of expressive programs written in Maude. Our partial evaluation scheme is based on an automatic unfolding algorithm that computes term variants and relies on high-performance order-sorted equational least general generalization and order-sorted equational homeomorphic embedding algorithms for ensuring termination. We show that our partial evaluation technique is sound and complete for convergent rewrite theories that may contain various combinations of associativity, commutativity, and/or identity axioms for different binary operators. We demonstrate the effectiveness of Maude's automatic partial evaluator, Victoria, on several examples where it shows significant speed-ups. (C) 2019 Elsevier Inc. All rights reserved.This work has been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by Generalitat Valenciana under grant PROMETEO/2019/098, and by NRL under contract number N00173-17-1-G002. Angel Cuenca-Ortega has been supported by the SENESCYT, Ecuador (scholarship program 2013).Alpuente Frasnedo, M.; Cuenca-Ortega, AE.; Escobar Román, S.; Meseguer, J. (2020). A Partial Evaluation Framework for Order-sorted Equational Programs modulo Axioms. Journal of Logical and Algebraic Methods in Programming. 110:1-36. https://doi.org/10.1016/j.jlamp.2019.100501S13611