State machines for large scale computer software and systems

A method for specifying the behavior and architecture of discrete state systems such as digital electronic devices and software using deterministic state machines and automata products. The state machines are represented by sequence maps $f:A^*\to X$ where $f(s)=x$ indicates that the output of the system is $x$ in the state reached by following the sequence of events $s$ from the initial state. Examples provided include counters, networks, reliable message delivery, real-time analysis of gates and latches, and producer/consumer. Techniques for defining, parameterizing, characterizing abstract properties, and connecting sequence functions are developed. Sequence functions are shown to represent (possibly non-finite) Moore type state machines and general products of state machines. The method draws on state machine theory, automata products, and recursive functions and is ordinary working mathematics, not involving formal methods or any foundational or meta-mathematical techniques. Systems in which there are levels of components that may operate in parallel or concurrently are specified in terms of function composition

Working with simple machines

A set of examples is provided that illustrate the use of work as applied to simple machines. The ramp, pulley, lever and hydraulic press are common experiences in the life of a student and their theoretical analysis therefore makes the abstract concept of work more real. The mechanical advantage of each of these systems is also discussed so that students can evaluate their usefulness as machines.Comment: 9 pages, 4 figure

Neurocognitive Informatics Manifesto.

Informatics studies all aspects of the structure of natural and artificial information systems. Theoretical and abstract approaches to information have made great advances, but human information processing is still unmatched in many areas, including information management, representation and understanding. Neurocognitive informatics is a new, emerging field that should help to improve the matching of artificial and natural systems, and inspire better computational algorithms to solve problems that are still beyond the reach of machines. In this position paper examples of neurocognitive inspirations and promising directions in this area are given

From Operational Semantics to Abstract Machines

We consider the problem of mechanically constructing abstract machines from operational semantics, producing intermediate-level specifications of evaluators guaranteed to be correct with respect to the operational semantics. We construct these machines by repeatedly applying correctness-preserving transformations to operational semantics until the resulting specifications have the form of abstract machines. Though not automatable in general, this approach to constructing machine implementations can be mechanized, providing machine-verified correctness proofs. As examples we present the transformation of specifications for both call-by-name and call-by-value evaluation of the untyped λ-calculus into abstract machines that implement such evaluation strategies. We also present extensions to the call-by-value machine for a language containing constructs for recursion, conditionals, concrete data types, and built-in functions. In all cases, the correctness of the derived abstract machines follows from the (generally transparent) correctness of the initial operational semantic specification and the correctness of the transformations applied

Robustness Verification of Support Vector Machines

We study the problem of formally verifying the robustness to adversarial examples of support vector machines (SVMs), a major machine learning model for classification and regression tasks. Following a recent stream of works on formal robustness verification of (deep) neural networks, our approach relies on a sound abstract version of a given SVM classifier to be used for checking its robustness. This methodology is parametric on a given numerical abstraction of real values and, analogously to the case of neural networks, needs neither abstract least upper bounds nor widening operators on this abstraction. The standard interval domain provides a simple instantiation of our abstraction technique, which is enhanced with the domain of reduced affine forms, which is an efficient abstraction of the zonotope abstract domain. This robustness verification technique has been fully implemented and experimentally evaluated on SVMs based on linear and nonlinear (polynomial and radial basis function) kernels, which have been trained on the popular MNIST dataset of images and on the recent and more challenging Fashion-MNIST dataset. The experimental results of our prototype SVM robustness verifier appear to be encouraging: this automated verification is fast, scalable and shows significantly high percentages of provable robustness on the test set of MNIST, in particular compared to the analogous provable robustness of neural networks

Semantic closure demonstrated by the evolution of a universal constructor architecture in an artificial chemistry

We present a novel stringmol-based artificial chemistry system modelled on the universal constructor architecture (UCA) first explored by von Neumann. In a UCA, machines interact with an abstract description of themselves to replicate by copying the abstract description and constructing the machines that the abstract description encodes. DNA-based replication follows this architecture, with DNA being the abstract description, the polymerase being the copier, and the ribosome being the principal machine in expressing what is encoded on the DNA. This architecture is semantically closed as the machine that defines what the abstract description means is itself encoded on that abstract description. We present a series of experiments with the stringmol UCA that show the evolution of the meaning of genomic material, allowing the concept of semantic closure and transitions between semantically closed states to be elucidated in the light of concrete examples. We present results where, for the first time in an in silico system, simultaneous evolution of the genomic material, copier and constructor of a UCA, giving rise to viable offspring

Instruction sequence processing operators

Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction between these behaviours and components of the execution environment, and two issues relating to computability theory. Positioning Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines, and taking instruction sequences as programs, we analyse the autosolvability requirement that a program of a certain kind must solve the halting problem for all programs of that kind. We present novel results concerning this autosolvability requirement. The analysis is streamlined by using the notion of a functional unit, which is an abstract state-based model of a machine. In the case where the behaviours exhibited by a component of an execution environment can be viewed as the behaviours of a machine in its different states, the behaviours concerned are completely determined by a functional unit. The above-mentioned analysis involves functional units whose possible states represent the possible contents of the tapes of Turing machines with a particular tape alphabet. We also investigate functional units whose possible states are the natural numbers. This investigation yields a novel computability result, viz. the existence of a universal computable functional unit for natural numbers.Comment: 37 pages; missing equations in table 3 added; combined with arXiv:0911.1851 [cs.PL] and arXiv:0911.5018 [cs.LO]; introduction and concluding remarks rewritten; remarks and examples added; minor error in proof of theorem 4 correcte