Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing and energy consumption, and the automatic synthesis of systems from specifications. The major challenges include environment modeling, incompleteness in specifications, and the complexity of underlying decision problems. This position paper proposes sciduction, an approach to tackle these challenges by integrating inductive inference, deductive reasoning, and structure hypotheses. Deductive reasoning, which leads from general rules or concepts to conclusions about specific problem instances, includes techniques such as logical inference and constraint solving. Inductive inference, which generalizes from specific instances to yield a concept, includes algorithmic learning from examples. Structure hypotheses are used to define the class of artifacts, such as invariants or program fragments, generated during verification or synthesis. Sciduction constrains inductive and deductive reasoning using structure hypotheses, and actively combines inductive and deductive reasoning: for instance, deductive techniques generate examples for learning, and inductive reasoning is used to guide the deductive engines. We illustrate this approach with three applications: (i) timing analysis of software; (ii) synthesis of loop-free programs, and (iii) controller synthesis for hybrid systems. Some future applications are also discussed

Layered cellular automata for pseudorandom number generation

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set formed by the transformation matrix of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L=1,2,3,4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions and in place of the linear function used in the L-LCA. Linear complexity is significantly increased when or is used

Towards Autopoietic Computing

A key challenge in modern computing is to develop systems that address complex, dynamic problems in a scalable and efficient way, because the increasing complexity of software makes designing and maintaining efficient and flexible systems increasingly difficult. Biological systems are thought to possess robust, scalable processing paradigms that can automatically manage complex, dynamic problem spaces, possessing several properties that may be useful in computer systems. The biological properties of self-organisation, self-replication, self-management, and scalability are addressed in an interesting way by autopoiesis, a descriptive theory of the cell founded on the concept of a system's circular organisation to define its boundary with its environment. In this paper, therefore, we review the main concepts of autopoiesis and then discuss how they could be related to fundamental concepts and theories of computation. The paper is conceptual in nature and the emphasis is on the review of other people's work in this area as part of a longer-term strategy to develop a formal theory of autopoietic computing.Comment: 10 Pages, 3 figure

Using formal methods to support testing

Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing

Presburger arithmetic, rational generating functions, and quasi-polynomials

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be represented by rational generating functions; a geometric characterization of such sets is also given. In addition, if p=(p_1,...,p_n) are a subset of the free variables in a Presburger formula, we can define a counting function g(p) to be the number of solutions to the formula, for a given p. We show that every counting function obtained in this way may be represented as, equivalently, either a piecewise quasi-polynomial or a rational generating function. Finally, we translate known computational complexity results into this setting and discuss open directions.Comment: revised, including significant additions explaining computational complexity results. To appear in Journal of Symbolic Logic. Extended abstract in ICALP 2013. 17 page

COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)