A Two-Layer Approach to the Computability and Complexity of Real Numbers

We present a new approach to computability of real numbers in which real functions have type-1 representations, which also includes the ability to reason about the complexity of real numbers and functions. We discuss how this allows efficient implementations of exact real numbers and also present a new real number system that is based on it

Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas

Online On-the-Fly Testing of Real-time Systems

In this paper we present a framework, an algorithm and a new tool for online testing of real-time systems based on symbolic techniques used in UPPAAL model checker. We extend UPPAAL timed automata network model to a test specification which is used to generate test primitives and to check the correctness of system responses including the timing aspects. We use timed trace inclusion as a conformance relation between system and specification to draw a test verdict. The test generation and execution algorithm is implemented as an extension to UPPAAL and experiments carried out to examine the correctness and performance of the tool. The experiment results are promising

Online On-the-Fly Testing of Real-time Systems

In this paper we present a framework, an algorithm and a new tool for online testing of real-time systems based on symbolic techniques used in UPPAAL model checker. We extend UPPAAL timed automata network model to a test specification which is used to generate test primitives and to check the correctness of system responses including the timing aspects. We use timed trace inclusion as a conformance relation between system and specification to draw a test verdict. The test generation and execution algorithm is implemented as an extension to UPPAAL and experiments carried out to examine the correctness and performance of the tool. The experiment results are promising

Bounds on Iterations of Asymptotically Quasi-Nonexpansive Mappings

Abstract. This paper establishes explicit quantitative bounds on the com-putation of approximate xed points of asymptotically (quasi-)nonexpansive mappings f by means of iterative processes. Here f: C! C is a selfmapping of a convex subset C X of a uniformly convex normed space X. We con-sider general Krasnoselski-Mann iterations with and without error terms. As a consequence of our quantitative analysis we also get new qualitative results which show that the assumption on the existence of xed points of f can be replaced by the existence of approximate xed points only. We explain how the existence of eective uniform bounds in this context can be inferred already a-priorily by a logical metatheorem recently proved by the rst author. Our bounds were in fact found with the help of the general logical machinery be-hind the proof of this metatheorem. The proofs we present here are, however, completely selfcontained and do not require any tools from logic. 1

Bounds on Iterations of Asymptotically Quasi-Nonexpansive Mappings

This paper establishes explicit quantitative bounds on the computation of approximate fixed points of asymptotically (quasi-) nonexpansive mappings f by means of iterative processes. Here f is a selfmapping of a convex subset C of a uniformly convex normed space X. We consider general Krasnoselski-Mann iterations with and without error terms. As a consequence of our quantitative analysis we also get new qualitative results which show that the assumption on the existence of fixed points of f can be replaced by the existence of approximate fixed points only. We explain how the existence of effective uniform bounds in this context can be inferred already a-priorily by a logical metatheorem recently proved by the first author. Our bounds were in fact found with the help of the general logical machinery behind the proof of this metatheorem. The proofs we present here are, however, completely self-contained and do not require any tools from logic

Pragmatics of Modular SOS

Modular SOS is a recently-developed variant of Plotkin's Structural Operational Semantics (SOS) framework. It has several pragmatic advantages over the original framework--the most significant being that rules specifying the semantics of individual language constructs can be given definitively, once and for all. Modular SOS is being used for teaching operational semantics at the undergraduate level. For this purpose, the meta-notation for modular SOS rules has been made more user-friendly, and derivation of computations according to the rules is simulated using Prolog. After giving an overview of the foundations of Modular SOS, this paper gives some illustrative examples of the use of the framework, and discusses various pragmatic aspects

The Small-Is-Very-Small Principle

The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable cut, then it shows that the property has a very small witness: i.e. a witness below a given standard number. We draw various consequences from the central result. For example (in rough formulations): (i) Every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative w.r.t. formulas of complexity $\leq n$. (ii) Every sequential model has, for any $n$, an extension that is elementary for formulas of complexity $\leq n$, in which the intersection of all definable cuts is the natural numbers. (iii) We have reflection for $\Sigma^0_2$-sentences with sufficiently small witness in any consistent restricted theory $U$. (iv) Suppose $U$ is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential $V$ that locally inteprets $U$, globally interprets $U$. Then, $U$ is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations

Danfoss EKC Trial Project Deliverables

This report documents the results of the Danfoss EKC trial project on model based development using IAR visualState. We present a formal state-model of a refrigeration controller based on a specification given by Danfoss. We report results on modeling, verification, simulation, and code-generation. It is found that the IAR visualState is a promising tool for this application domain, but that improvements must be done to code-generation and automatic test generation

Composing Programming Languages by Combining Action-Semantics Modules

This article demonstrates a method for composing a programming language by combining action-semantics modules. Each module is defined separately, and then a programming-language module is defined by combining existing modules. This method enables the language designer to gradually develop a language by defining, selecting and combining suitable modules. The resulting modular structure is substantially different from that previously employed in action-semantic descriptions. It also discusses how to resolve the conflicts that may arise when combining modules, and indicates some advantages that action semantics has over other approaches in this respect