María-José Hidalgo

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We present an application of the ACL2 theorem prover to reason about rewrite systems theory. We describe the formalization and representation aspects of our work using the first-order, quantifier-free logic of ACL2 and we sketch some of the main points of the proof effort. First, we present a formalization of abstract reduction systems and then we show how(More)
This paper describes a mathematical tool for local identifiability analysis that can easily be applied to high-order state-space nonlinear systems and implemented in simulators with a discrete-time approach. The methodology is based on the recursive numerical evaluation of a reduced information matrix during the simulation of a calibration experiment and in(More)
The Ontology Web Language (OWL) is a language used for the Semantic Web. OWL is based on Description Logics (DLs), a family of logical formalisms for representing and reasoning about conceptual and terminological knowledge. Among these, the logic ALC is a ground DL used in many practical cases. Moreover, the Semantic Web appears as a new field for the(More)
We present a case study using ACL2 [5] to verify a non-trivial algorithm that uses efficient data structures. The algorithm receives as input two first-order terms and it returns a most general unifier of these terms if they are unifiable, failure otherwise. The verified implementation stores terms as directed acyclic graphs by means of a pointer structure.(More)
Dickson's Lemma is the main result needed to prove the termination of Buchberger's algorithm for computing Gröbner basis of polynomial ideals. In this case study, we present a formal proof of Dickson's Lemma using the ACL2 system. Due to the limited expressiveness of the ACL2 logic, the classical non-constructive proof of this result cannot be done in ACL2.(More)
In this paper we present a formalization and proof of Hig-man's Lemma in ACL2. We formalize the constructive proof described in [10] where the result is proved using a termination argument justified by the multiset extension of a well-founded relation. To our knowledge, this is the first mechanization of this proof.
This paper describes a mathematical tool for identifiability analysis, easily applicable to high order non-linear systems modelled in state-space and implementable in simulators with a time-discrete approach. This procedure also permits a rigorous analysis of the expected estimation errors (average and maximum) in calibration experiments. The methodology is(More)
We present in this paper an application of the ACL2 system to reason about propositional satisfiability provers. For that purpose, we present a framework where we define a generic transformation based SAT–prover, and we show how this generic framework can be formalized in the ACL2 logic, making a formal proof of its termination, soundness and completeness.(More)