Specification of Adleman’s Restricted Model Using an Automated Reasoning System: Verification of Lipton’s Experiment

The aim ofthis paper is to develop an executable prototype ofan unconventional model ofcomputation. Using the PVS verification system (an interactive environment for writing formal specifications and checking formal proofs), we formalize the restricted model, based on DNA, due to L. Adleman. Also, we design a formal molecular program in this model that solves SAT following Lipton’s ideas.We prove using PVS the soundness and completeness ofthis molecular program. This work is intended to give an approach to the opportunities offered by mechanized analysis ofuncon ventional model ofcomputation in general. This approach opens up new possibilities ofv erifying molecular experiments before implementing them in a laboratory.Ministerio de Educación y Cultura TIC2000-1368-C03-02Ministerio de Educación y Cultura PB96-134

Rete Algorithm Applied to Robotic Soccer

This article is a first approach to the use of Rete algorithm to design a team of robotic soccer playing agents for Robocup Soccer Server. Rete algorithm is widely used to design rule-based expert systems. Robocup Soccer Server is a system that simulates 2D robotic soccer matches. The paper presents an architecture based on CM United team architecture for Robocup Soccer Server simulation system. It generalizes the low-level information received by the agent as high-level soccer concepts. This way it can take advantage of expert system design techniques

ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System

Kenzo is a Computer Algebra system devoted to Algebraic Topology, and written in the Common Lisp programming language. It is a descendant of a previous system called EAT (for Effective Algebraic Topology). Kenzo shows a much better performance than EAT due, among other reasons, to a smart encoding of degeneracy lists as integers. In this paper, we give a complete automated proof of the correctness of this encoding used in Kenzo. The proof is carried out using ACL2, a system for proving properties of programs written in (a subset of) Common Lisp. The most interesting idea, from a methodological point of view, is our use of EAT to build a model on which the verification is carried out. Thus, EAT, which is logically simpler but less efficient than Kenzo, acts as a mathematical model and then Kenzo is formally verified against it.Ministerio de Educación y Ciencia MTM2006-0651

Expert System to Real Time Control of Machining Processes

Industrial machining processes use automated milling machines. These machines are connected to a control device that provides the basic instructions used to obtain a piece. However, these processes depend on the human decision to diagnose and correct in real time the inaccuracies that can occur. In this work we present an expert system to real time control of machining processes using the information provided by sensors located on the machine. This system has been implemented as a prototype in a Kondia 600 milling machine with a FAGOR 8025-MG control device

KRRT: Knowledge Representation and Reasoning Tutor System

Knowledge Representation & Reasoning (KR&R) is a fundamental topic in Artificial Intelligence. A basic KR language is First– Order Logic (FOL), the most representative logic–based representation language, which is part of almost any introductory AI course. In this work we present KRRT (Knowledge Representation & Reasoning Tutor). KRRT is a Web–based system which main goal is to help the student to learn FOL as a KR&R language.Ministerio de Educación y Ciencia TIN2004–0388

Molecular Computation Models in ACL2: a Simulation of Lipton’s Experiment Solving SAT

In this paper we present an ACL2 formalization of a molecular computing model: Adleman’s restricted model [2]. This is a first step to formalize unconventional models of computation in ACL2. As an application of this model, an implementation of Lipton’s experiment solving SAT [7] is described, based on the formalization given in [6]. We use ACL2 to make a formal proof of the completeness and soundness properties of the function implementing the experimentMinisterio de Ciencia y Tecnología TIC2000-1368-CO3-0

Certified Symbolic Manipulation: Bivariate Simplicial Polynomials

Certified symbolic manipulation is an emerging new field where programs are accompanied by certificates that, suitably interpreted, ensure the correctness of the algorithms. In this paper, we focus on algebraic algorithms implemented in the proof assistant ACL2, which allows us to verify correctness in the same programming environment. The case study is that of bivariate simplicial polynomials, a data structure used to help the proof of properties in Simplicial Topology. Simplicial polynomials can be computationally interpreted in two ways. As symbolic expressions, they can be handled algorithmically, increasing the automation in ACL2 proofs. As representations of functional operators, they help proving properties of categorical morphisms. As an application of this second view, we present the definition in ACL2 of some morphisms involved in the Eilenberg-Zilber reduction, a central part of the Kenzo computer algebra system. We have proved the ACL2 implementations are correct and tested that they get the same results as Kenzo does.Ministerio de Ciencia e Innovación MTM2009-13842Unión Europea nr. 243847 (ForMath

Verifying the bridge between simplicial topology and algebra: the Eilenberg–Zilber algorithm

The Eilenberg–Zilber algorithm is one of the central components of the computer algebra system called Kenzo, devoted to computing in Algebraic Topology. In this article we report on a complete formal proof of the underlying Eilenberg–Zilber theorem, using the ACL2 theorem prover. As our formalization is executable, we are able to compare the results of the certified programme with those of Kenzo on some universal examples. Since the results coincide, the reliability of Kenzo is reinforced. This is a new step in our long-term project towards certified programming for Algebraic Topology.Ministerio de Ciencia e Innovación MTM2009-13842European Union’s 7th Framework Programme [243847] (ForMath)

Applying ACL2 to the Formalization of Algebraic Topology: Simplicial Polynomials

In this paper we present a complete formalization, using the ACL2 theorem prover, of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. The interest of this work stems from three sources. First, the normalization theorem is the basis for some design decisions in the Kenzo computer algebra system, a program for computing in Algebraic Topology. Second, our proof of the theorem is new and shows the correctness of some formulas found experimentally, giving explicit expressions for the above-mentioned homotopy equivalence. And third, it demonstrates that the ACL2 theorem prover can be effectively used to formalize mathematics, even in areas where higher-order tools could be thought to be more appropriate.Ministerio de Ciencia e Innovación MTM2009-13842European Commission FP7 STREP project ForMath n. 24384

Formalization of a normalization theorem in simplicial topology

In this paper we present a complete formalization of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. Even if the Normalization Theorem is usually stated as a higher-order result (with a Category Theory flavor) we manage to give a first-order proof of it. To this aim it is instrumental the introduction of an algebraic data structure called simplicial polynomial. As a demonstration of the validity of our techniques we developed a formal proof in the ACL2 theorem prover.Ministerio de Ciencia e Innovación MTM2009-13842European Commission FP7 STREP project ForMath n. 24384