Symbolic Techniques Research Articles

Loop Extended Symbolic Execution on List Manipulating Programs

Current symbolic execution is challenged by its ability to deal with loops. The case gets worse for loops manipulating recursive data structures. In this paper, we extend classic symbolic execution techniques for error detection of programs manipulating lists in loops. The idea is to enhance the symbolic execution with the utilization of quantitative aspect of the shape, and to construct the exit state of the loop. The exit state is constrained by a set of numeric constraints containing normal symbolic variables in programs and instrumented symbolic variables on the shapes. A prototype tool has been implemented and experiments are conducted on some commonly used list manipulating programs.

Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation

Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.

A survey on binary decision diagram approaches to symbolic analysis of analog integrated circuits

Applying symbolic techniques for analog circuit analysis is a traditional research subject, which has lasted for over half a century. The past decade has witnessed a significant advancement of the symbolic techniques developed specifically for large analog integrated circuits. The key methodology introduced is a data structure called binary decision diagram (BDD) which was established originally for logic design and verification. The application of the BDD technique for analog circuit analysis has the following features: (1) It is a compact data structure so that data redundancy in symbolic analysis can be eliminated. (2) It provides a mechanism for implicit enumeration method so that exhaustive enumeration commonly performed in symbolic analysis can be avoided. (3) Numerical evaluation on a BDD can be made extremely efficient, making it an excellent means for repetitive analysis. More advanced features are yet to be explored. This survey brings together the significant research results published in the past decade and provides a tutorial overview on the basic principles of applying BDD to analog circuit analysis. Some new directions that are potentially valuable for developing future analog design automation tools are discussed and a design example is given to illustrate the application of symbolic techniques.

Erratum. Use of reproducing kernels and Berezin symbols technique in some questions of operator theory

Erratum. Use of reproducing kernels and Berezin symbols technique in some questions of operator theory

Strategies for scalable symbolic execution-driven test generation for programs

With the advent of advanced program analysis and constraint solving techniques, several test generation tools use variants of symbolic execution. Symbolic techniques have been shown to be very effective in path-based test generation; however, they fail to scale to large programs due to the exponential number of paths to be explored. In this paper, we focus on tackling this path explosion problem and propose search strategies to achieve quick branch coverage under symbolic execution, while exploring only a fraction of paths in the program. We present a reachability-guided strategy that makes use of the reachability graph of the program to explore unvisited portions of the program and a conflict-driven backtracking strategy that utilizes conflict analysis to perform nonchronological backtracking. We present experimental evidence that these strategies can significantly reduce the search space and improve the speed of test generation for programs.

Space, Cyberspace and Interface: The Trouble with Google Maps

Space, Cyberspace and Interface: The Trouble with Google Maps

Block-Entropy Analysis of Climate Data

We explore the use of block entropy as a dynamics classifier for meteorological timeseries data. The block entropy estimates define the entropy growth curve H(L) with respect to block length L. For a finitary process, the entropy growth curve tends to an asymptotic linear regime H(L) = E + hμL, with entropy rate hμ and excess entropy E. These quantities apportion the system's information content into ‘memory’ (E) and ‘randomness’ (hμ). We discuss the challenges inherent in analyzing weather data using symbolic techniques, identifying the pitfalls associated with alphabet size, finite sample timeseries length, and stationarity. We apply the block entropy-based techniques in the form of a wet/dry partition to Australian daily precipitation data from the Patched Point Dataset station record collection and version 3 of the Australian Water Availability Project analysis dataset. Preliminary results demonstrate hμ and E are viable climatological classifiers for precipitation, with station records from similar climatic regimes possessing similar values of hμ and E. The resultant clustering reflects expected characteristics of local climatic memory and randomness. The AWAP results show weaker clustering than their PPD counterparts, with different E- and hμ-values reflecting respectively the relative biases and truncation errors in the AWAP analysis system. The entropy rates of convergence analysis rules out finite order Markov processes for orders falling within the range of block sizes considered.

On Abel Convergence of Double Sequences

In terms of Berezin symbols, we give the concept of (Ber)-convergence of bounded double sequences. We prove that every (Ber)-convergent double sequence is Abel convergent. In particular, by using the Berezin symbols technique, we prove the following double sequence analog of the classical Abel theorem for the sequences: If the sequence regularly converges to L, then

High-precision numerical integration: Progress and challenges

One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead.

Abstract only

Polynomial homotopy continuation is at the heart of numerical algebraic geometry, an area whose primary goal is to solve systems of polynomial equations. Recently this field developed rapidly producing several software packages that solve some problems out of reach for purely symbolic techniques. However, the homotopy tracking procedures employ heuristics to follow the homotopy continuation paths. Jointly with Carlos Beltran we have devised a certified homotopy tracking algorithm, which was implemented in Macaulay2. In addition we conducted experiments shedding light on some developments in complexity analysis of polynomial systems solving.

Coincidences in chemical kinetics: Surprising news about simple reactions

New properties of intersections and coincidences of transient concentration curves were discovered and are presented analytically using the classical consecutive mechanism A → B → C as an example. We identify six different special points, and analyze and classify the six possible (out of 612 combinations) patterns of concentration peak and intersection times and values that distinguish the parameter subdomains and sometimes can eliminate the mechanism. This developed theory is tested on examples (multi-step radioactive decay, isomerization reaction). The mathematical analysis relies on a combination of elementary and symbolic techniques, special functions and numerical approximations.

A hierarchical framework for logical composition of web services

Automatically composing Web services to form processes in the context of service-oriented architectures has attracted significant research. Prevalent approaches for automatically composing Web services predominantly utilize planning techniques to achieve the composition. However, classical planning based approaches face the following challenges: (i) difficulty in modeling the uncertainty of Web service invocations, (ii) inability to optimize the composition using non-functional parameters, and (iii) difficulty in scaling efficiently to large compositions. In order to address these issues, we present a hierarchical framework for logically composing Web services, which we call Haley. In comparison to classical planners, Haley utilizes decision-theoretic planning that is able to model and reason with the uncertainty inherent in Web service invocations and provides an expected cost-based optimization. Haley uses symbolic planning techniques that operate directly on first-order logic based representations of the state space to obtain the compositions. Consequently, it supports automated elicitation of the corresponding planning problem from Web service descriptions and produces a domain representation that is more compact than that of classical planners. Furthermore, it promotes scalability by exploiting the natural hierarchy found in real-world processes. Due to the limitations of the existing approaches and the complexity of the Web service composition problem, few implemented tools exist, although many approaches have been proposed in the literature. We have implemented Haley and provided a comprehensive tool suite for composing Web services. The suite operates on Web services described using well-known languages such as SAWSDL. It provides process designers with an intuitive interface to specify composition requirements, goals and a hierarchical decomposition if available, and automatically generates BPEL compositions while hiding the complexity of the planning and of BPEL from users.

Method of implementing frequency-encoded NOT, OR and NOR logic operations using lithium niobate waveguide and reflecting semiconductor optical amplifiers

Optics has already proved its strong potentiality for the conduction of parallel logic, arithmetic and algebraic operations. In the last few decades several all-optical data processors were proposed. To implement these processors different data encoding/decoding techniques have been reported. In this context, polarization encoding technique, intensitybased encoding technique, tristate and quaternary logic operation, multivalued logic operations, symbolic substitution techniques etc. may be mentioned. Very recently, frequency encoding/decoding technique has drawn interest from the scientific community. Frequency is the fundamental character of any signal; and it remains unaltered in reflection, refraction, absorption etc. during the propagation and transmission of the signal. This is the most important advantage of frequency encoding technique over the conventional encoding techniques. In this communication the authors propose a new scheme for implementing NOT, OR and NOR logic operations. For this purpose co-propagating beams having different frequencies in C-band (1535–1560 nm) have been used for generating cascaded sum and difference frequency, exploiting the nonlinear response character of periodically poled LiNbO3 waveguide. The cross-gain modulation property of the semiconductor optical amplifier (SOA) and the wavelength conversion property of the reflecting semiconductor optical amplifiers (RSOA) are exploited here to implement the desired optical logic and arithmetic operations.

Heuristic and exact techniques for aircraft maintenance scheduling

Aircraft's availability is certainly one of the most important features of modern avionic industry. High availability can only be obtained with very efficient maintenance cycles. These cycles, in turn, are extremely expensive in terms of tools and personnel. This article describes the main features of an aircraft maintenance cycle contrasting it with other similar scheduling tasks. After that, it demonstrates how to model a maintenance cycle to enable a symbolic (mathematical) analysis, and it shows how to create a plan with both heuristic and symbolic (exact) techniques. Heuristic techniques show high efficiency and scalability, but they deliver sub-optimal results, and are then unable to minimize maintenance costs. Exact techniques are able to find optimal solutions even for very constrained tasks. Unfortunately, even the most efficient exact strategy is not able to deal with real (complete) maintenance problems. As a consequence, heuristic and exact strategies are used together to trade-off the accuracy of the result with the capacity of the considered problems. From the experimental point of view, the article reports data on real maintenance tasks coming from the avionic industry. It describes how to discover and to correct error coded in the original database, which all previous manual analyses were unable to reveal. The final scheduling shows consistent improvements against the original manual planning adopted on the field so far.

An algebraic operator approach to the analysis of Gerber–Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber–Shiu function in terms of the penalty function.

Model checking race-freeness

With the introduction of highly concurrent systems in standard desktop computers, ensuring correctness of industrial-size concurrent programs is becoming increasingly important. One of the most important standards in use for developing multi-threaded programs is the POSIX Threads standard, commonly known as PThreads. Of particular importance, the analysis of industrial code should, as far as possible, be automatic and not require annotations or other forms of specifications of the code. Model checking has been one of the most successful approaches to program verification during the last two decades. The size and complexity of applications which can be handled have increased rapidly through integration with symbolic techniques. These methods are designed to work on finite (but large) state spaces. This framework fails to deal with several essential aspects of behaviours for multithreaded programs: there is no bound a priori on the number of threads which may arise in a given run of the system; each thread manipulates local variables which often range over unbounded domains; and the system has a dynamic structure in the sense that threads can be created and killed throughout execution of the system. In this paper we concentrate on checking a particular class of properties for concurrent programs, namely safety properties. In particular, we focus on race-freeness, that is, the absence of race conditions (also known as data races) in shared-variable pthreaded programs. We will follow a particular methodology which we have earlier developed for model checking general classes of infinite-state systems [1, 3, 6, 8, 9] and apply a symbolic backward reachability analysis to verify the safety property. Since we construct a model as an over-approximation of the original program, proving the safety property in the model implies that the property also holds in the original system. Surprisingly, it leads to a quite efficient analysis which can be carried out fully automatically.

The Algebra of Connectors—Structuring Interaction in BIP

We provide an algebraic formalization of connectors in the BIP component framework. A connector relates a set of typed ports. Types are used to describe different modes of synchronization: rendezvous and broadcast, in particular. Connectors on a set of ports P are modeled as terms of the algebra AC(P), generated from P by using a binary fusion operator and a unary typing operator. Typing associates with terms (ports or connectors) synchronization types --- trigger or synchron --- that determine modes of synchronization. Broadcast interactions are initiated by triggers. Rendezvous is a maximal interaction of a connector including only synchrons. The semantics of AC(P) associates with a connector the set of its interactions. It induces on connectors an equivalence relation which is not a congruence as it is not stable for fusion. We provide a number of properties of AC(P) used to symbolically simplify and handle connectors. We provide examples illustrating applications of AC(P), including a general component model encompassing synchrony, methods for incremental model decomposition, and efficient implementation by using symbolic techniques.

Proving Correctness of an Efficient Abstraction for Interrupt Handling

This paper presents an approach to the efficient abstraction of interrupt handling in microcontroller systems. Such systems usually operate in uncertain environments, giving rise to a high degree of nondeterminism in the corresponding formal models, which in turn aggravates the state explosion problem. Careful handling of nondeterminism is therefore crucial for obtaining efficient model checking tools. Here, we support this goal by developing a formal computation model and an abstraction method, called interrupt nondeterminism, which instantiates nondeterministic values only if and when this is required by the application code. It is shown how this symbolic technique can be integrated into our explicit CTL model checking tool [mc]square by introducing lazy states. A lazy state consists of explicit and symbolic parts and therefore, represents several concrete states. With regard to interrupt handling, we also give a simulation relation between the concrete and the abstract state space, thus establishing the correctness of our technique. Furthermore, a case study is presented in which three different programs are used to demonstrate the effectiveness of our method.

Symbolic Reduction for High-Speed Power System Simulation

High-speed simulations of power transmission systems, which often rely on solving nonlinear systems of equations, are an increasingly important tool for training, testing equipment, on-line control and situational awareness. Such simulations, however, suffer from two major problems: (1) they can be too computationally demanding to simulate large, complex systems within appropriate time constraints; and (2) they are difficult to develop and debug. Prior work has shown how symbolic computation can be used to help reduce both problems. In this paper, we: (1) review common concepts in power system simulations; (2) summarize prior use of symbolic computation in power system simulation; (3) explore the advantages and disadvantages achieved via symbolic techniques; (4) extend the techniques to solve linear systems via a priori symbolic LU decomposition; and (5) demonstrate the advantages of symbolic techniques on a transient event simulation of the IEEE 118-bus test power system, which runs in one-tenth the time of an equivalent traditional (sparse matrix) approach.

Genericity in topological dynamics

AbstractWe study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner–King type correspondence: genericity in one is equivalent to genericity in the other. By applying symbolic techniques in the shift-space model we derive new results about genericity of dynamical properties for transitive and totally transitive homeomorphisms of the Cantor set. We show that the isomorphism class of the universal odometer is generic in the space of transitive systems. On the other hand, the space of totally transitive systems displays much more varied dynamics. In particular, we show that in this space the isomorphism class of every Cantor system without periodic points is dense and the following properties are generic: minimality, zero entropy, disjointness from a fixed totally transitive system, weak mixing, strong mixing and minimal self joinings. The latter two stand in striking contrast to the situation in the measure-preserving category. We also prove a correspondence between genericity of dynamical properties in the measure-preserving category and genericity of systems supporting an invariant measure with the same property.