Canonical Narrowing with Irreducibility Constraints as a Symbolic Protocol Analysis Method

Narrowing and heuristic search for symbolic reachability analysis of concurrent object-oriented systems

In this paper, we propose a novel symbolic analysis method for analog behavioral modeling by Boolean logic operations and graph representation. The exact symbolic analysis problem is formulated as a logic circuit synthesis problem where we build a logic circuit, which detects whether or not a given symbolic term is a valid product term from a determinant. The logic circuit is represented by binary decision diagrams (BDDs), which can be trivially transformed into zero-suppressed binary decision diagrams (ZBDDs). ZBDDs are essentially determinant decision diagrams (DDDs) representation of a determinant. The significance of the new method is that all product terms can be constructed implicitly and simultaneously, in contrast to all previous symbolic analysis methods where symbolic terms are generated explicitly and sequentially by Laplace expansion or topological methods. We further apply the logic synthesis idea to generating symbolic coefficients of s-expanded polynomials and present a method to compute coefficients individually and selectively. Our new approach demonstrates an inherent relationship between circuit simulation and logic synthesis for the first time. Experimental results show the speedup of our new method over the existing flat method and its greater capacity over both existing flat and hierarchical symbolic analyzers.

This paper introduces$\tt{{Presto}}$, a symbolic partial evaluator for Maude’s rewriting logic theories that can improve system analysis and verification. In$\tt{{Presto}}$, the automated optimization of a conditional rewrite theory$\mathcal{R}$(whose rules define the concurrent transitions of a system) is achieved by partially evaluating, with respect to the rules of$\mathcal{R}$, an underlying, companion equational logic theory$\mathcal{E}$that specifies the algebraic structure of the system states of$\mathcal{R}$. This can be particularly useful for specializing an overly general equational theory$\mathcal{E}$whose operators may obey complex combinations of associativity, commutativity, and/or identity axioms, when being plugged into a host rewrite theory$\mathcal{R}$as happens, for instance, in protocol analysis, where sophisticated equational theories for cryptography are used.$\tt{{Presto}}$implements different unfolding operators that are based onfolding variant narrowing(the symbolic engine of Maude’s equational theories). When combined with an appropriate abstraction algorithm, they allow the specialization to be adapted to the theory termination behavior and bring significant improvement while ensuring strong correctness and termination of the specialization. We demonstrate the effectiveness of$\tt{{Presto}}$in several examples of protocol analysis where it achieves a significant speed-up. Actually, the transformation provided by$\tt{{Presto}}$may cut down an infinite folding variant narrowing space to a finite one, and moreover, some of the costly algebraic axioms and rule conditions may be eliminated as well. As far as we know, this is the first partial evaluator for Maude that respects the semantics of functional, logic, concurrent, and object-oriented computations.

Industrial analog circuits are usually designed using numerical simulation tools. To obtain a deeper circuit understanding, symbolic analysis techniques can additionally be applied. Approximation methods which reduce the complexity of symbolic expressions are needed in order to handle industrial-sized problems. This paper describes aspects of the field of symbolic analog circuit analysis. Some state-of-the-art simplification algorithms for linear and nonlinear circuits are presented. The basic ideas behind the different techniques are described and two application examples for the linear and nonlinear case will be demonstrated.

The open calculus of constructions integrates key features of Martin-Löf's type theory, the calculus of constructions, membership equational logic, and rewriting logic into a single uniform language. The two key ingredients are dependent function types and conditional rewriting modulo equational theories. We explore the open calculus of constructions as a uniform framework for programming, specification and interactive verification in an equational higher-order style. By having equational logic and rewriting logic as executable sublogics we preserve the advantages of a first-order semantic and logical framework and we provide a foundation for a broad spectrum of applications ranging from what could be called executable mathematics, involving symbolic computations and logical proofs, to software and system engineering applications, involving symbolic execution and analysis of nondeterministic and concurrent systems.

In this paper, a new appearance-based technique called symbolic factorial discriminant analysis (symbolic FDA) is explored for face representation and recognition under varying illumination conditions. In the past few years, many appearance-based methods have been proposed to model image variations of human faces under different lighting conditions using single valued variables to represent the facial features. In the proposed symbolic factorial discriminant analysis method, we extract interval type discriminating features, which are robust to illumination changes. The minimum distance classifier with symbolic dissimilarity measure is used for classification. The proposed method has been successfully tested for face recognition using three databases, namely, Yale Face database B, CMU PIE database and Harvard database. The experimental results have demonstrated the effective performance of this method.

Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free satisfiability in the initial algebra of an order-sorted equational theory \((\varSigma ,E \cup B)\) under two conditions: (i) \(E \cup B\) has the finite variant property and B has a finitary unification algorithm; and (ii) \((\varSigma ,E \cup B)\) protects a constructor subtheory \((\varOmega ,E_{\varOmega } \cup B_{\varOmega })\) that is OS-compact. These conditions apply to many user-definable theories, but have a main limitation: they apply well to data structures, but often do not hold for user-definable predicates on such data structures. We present a theory-generic satisfiability decision procedure, and a prototype implementation, extending variant-based satisfiability to initial algebras with user-definable predicates under fairly general conditions.

We can model embedded systems as hybrid systems. Moreover, they are distributed and real-time systems. Therefore, it is important to specify and verify randomness and soft real-time properties. For the purpose of system verification, we formally define probabilistic linear hybrid automaton and its symbolic reachability analysis method. It can describe uncertainties and soft real-time characteristics. Our proposal method is the first attempt to symbolically verify probabilistic linear hybrid automata.KeywordsModel CheckLogical FormulaDiscrete TransitionHybrid AutomatonReachability AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We can model embedded systems as hybrid systems. Moreover, they are distributed and real-time systems. Therefore, it is important to specify and verify randomness and soft real-time properties. For the purpose of system verification, we formally define probabilistic linear hybrid automaton and its symbolic reachability analysis method. It can describe uncertainties and soft real-time characteristics.

Symbolic circuit analysis using Mathematics A method of symbolic circuit analysis using Mathematica is reported. With the powerful symbolic manipulation capacity of Mathematica, symbolic circuit analysis is significantly simplified. The analysed circuits can be passive or active, with active devices modelled by nullors. Non-trivial circuit analysis examples are presented and the program list is given.

Equational unification and matching are fundamental mechanisms in many automated deduction applications. Supporting them efficiently for as wide as possible a class of equational theories, and in a typed manner supporting type hierarchies, benefits many applications; but this is both challenging and nontrivial. We present Maude 3.2’s efficient support of these features as well as of symbolic reachability analysis of infinite-state concurrent systems based on them.

On the application of interval PCA to process monitoring: A robust strategy for sensor FDI with new efficient control statistics

In a fundamental paradigm shift in system design, entire systems are being built on a single chip, using multiple embedded cores. Though the newest system design methodology has several advantages in terms of time-to-market and system cost, testing such core-based systems is difficult, mainly due to the problem of justifying test sequences at the inputs of a core embedded deep in the circuit and propagating test responses from the core outputs. In this paper, we first present a design for testability technique for testing such core-based systems. In this scheme, untestable cores are first made testable using hierarchical testability analysis techniques. If necessary, additional testability hardware is added to the cores to make them transparent so that they can propagate test data without information loss. This testability and transparency technique is currently applicable to cores of the following types: application-specific integrated circuits, application-specific programmable processors, and application-specific instruction processors. Other core types can be made testable and transparent using traditional techniques. The testable and transparent cores can then he integrated together with some system-level testability hardware to ensure justification of precomputed test sequences of each core from system primary inputs to the core inputs and propagation of test responses from core outputs to system primary outputs. Justification and propagation of test sequences are done at the system level by extending and suitably modifying the symbolic hierarchical testability analysis method that has been successfully applied to register-transfer level circuits. Since the testability analysis method is symbolic, the system test generation method is independent of the bit-width of the cores. The system-level test set is obtained as a byproduct of the testability analysis and insertion method without further search. The test methodology was applied to six example systems. Besides the proposed test method, the two methods that are currently used in the industry were also evaluated: (1) FScan-BScan, where each core is full-scanned, and system test is performed using boundary scan and (2) FScan-TBus, where each core is full-scanned, and system test is performed using a test bus. The experiments show that the proposed scheme has significantly lower area overhead, delay overhead, and test application time compared to FScan-BScan and FScan-TBus, without any compromise in the system fault coverage.

Algebraic Observability Analysis of Electrical Network with Symbolic Computation: Application on MYRTE Electrical Power Plant

This study aims to analyze the representation of yōkai in the anime Mononoke (2007) as a visual manifestation of the characters’ psychological trauma. Unlike the portrayal of yōkai in traditional Japanese folklore—which tends to emphasize mythological or horror aspects—Mononoke reconstructs these figures as embodiments of unexpressed inner wounds such as guilt, repression, anger, and loss. This research employs a qualitative-descriptive approach with symbolic and narrative analysis methods, grounded in trauma theory as proposed by Cathy Caruth. The analysis reveals that yōkai in this anime function not merely as horror elements, but as media through which complex psychological conflicts are conveyed. Through symbolism, visual atmosphere, and metaphorical narrative structure, Mononoke gives voice to trauma that cannot be articulated directly. As such, the anime does not simply depict supernatural beings but serves as a reflective space that connects folklore, psychology, and visual cultural expression. This study is expected to contribute to interdisciplinary understanding across Japanese cultural studies, literary psychology, and contemporary media analysis.