
Adolfo Piperno, and Enrico Tronci. "Regular Systems of Equations in λcalculus." Int. J. Found. Comput. Sci. 1, no. 3 (1990): 325–340. DOI: 10.1142/S0129054190000230.
Abstract: Many problems arising in equational theories like Lambdacalculus and Combinatory Logic can be expressed by combinatory equations or systems of equations. However, the solvability problem for an arbitrarily given class of systems is in general undecidable. In this paper we shall focus our attention on a decidable class of systems, which will be called regular systems, and we shall analyse some classical problems and wellknown properties of Lambdacalculus that can be described and solved by means of regular systems. The significance of such class will be emphasized showing that for slight extensions of it the solvability problem turns out to be undecidable.



Adolfo Piperno, and Enrico Tronci. "Regular Systems of Equations in λcalculus." In Ictcs. Mantova  Italy, 1989. DOI: 10.1142/S0129054190000230.
Abstract: Many problems arising in equational theories like Lambdacalculus and Combinatory Logic can be expressed by combinatory equations or systems of equations. However, the solvability problem for an arbitrarily given class of systems is in general undecidable. In this paper we shall focus our attention on a decidable class of systems, which will be called regular systems, and we shall analyse some classical problems and wellknown properties of Lambdacalculus that can be described and solved by means of regular systems. The significance of such class will be emphasized showing that for slight extensions of it the solvability problem turns out to be undecidable.



Corrado BÃ¶hm, Adolfo Piperno, and Enrico Tronci. "Solving Equations in λcalculus." In Proc. of: Logic Colloquium 88. Padova  Italy, 1989.



Corrado BÃ¶hm, and Enrico Tronci. "XSeparability and LeftInvertibility in lambdacalculus." In Symposium on Logic in Computer Science (LICS), 320–328. Ithaca, New York, USA: IEEE Computer Society, 1987.



Corrado BÃ¶hm, and Enrico Tronci. "Xseparability and leftinvertibility in the λcalculus (extended abstract, invited paper)." In Proceedings of: Temi e prospettive della Logica e della Filosofia della Scienza contemporanea. Cesena  Italy, 1987.



Andrea Bobbio, Sandro Bologna, Michele Minichino, Ester Ciancamerla, Piero Incalcaterra, Corrado Kropp, and Enrico Tronci. "Advanced techniques for safety analysis applied to the gas turbine control system of Icaro co generative plant." In X Convegno Tecnologie e Sistemi Energetici Complessi, 339–350. Genova, Italy, 2001.
Abstract: The paper describes two complementary and integrable approaches, a probabilistic one and a deterministic one, based on classic and advanced modelling techniques for safety analysis of complex computer based systems. The probabilistic approach is based on classical and innovative probabilistic analysis methods. The deterministic approach is based on formal verification methods. Such approaches are applied to the gas turbine control system of ICARO co generative plant, in operation at ENEA CR Casaccia. The main difference between the two approaches, behind the underlining different theories, is that the probabilistic one addresses the control system by itself, as the set of sensors, processing units and actuators, while the deterministic one also includes the behaviour of the equipment under control which interacts with the control system. The final aim of the research, documented in this paper, is to explore an innovative method which put the probabilistic and deterministic approaches in a strong relation to overcome the drawbacks of their isolated, selective and fragmented use which can lead to inconsistencies in the evaluation results.



Enrico Tronci. "On Computing Optimal Controllers for Finite State Systems." In CDC '97: Proceedings of the 36th IEEE International Conference on Decision and Control. Washington, DC, USA: IEEE Computer Society, 1997.



Enrico Tronci. "Optimal Finite State Supervisory Control." In CDC '96: Proceedings of the 35th IEEE International Conference on Decision and Control. Washington, DC, USA: IEEE Computer Society, 1996. DOI: 10.1109/CDC.1996.572981.
Abstract: Supervisory Controllers are Discrete Event Dynamic Systems (DEDSs) forming the discrete core of a Hybrid Control System. We address the problem of automatic synthesis of Optimal Finite State Supervisory Controllers (OSCs). We show that Boolean First Order Logic (BFOL) and Binary Decision Diagrams (BDDs) are an effective methodological and practical framework for Optimal Finite State Supervisory Control. Using BFOL programs (i.e. systems of boolean functional equations) and BDDs we give a symbolic (i.e. BDD based) algorithm for automatic synthesis of OSCs. Our OSC synthesis algorithm can handle arbitrary sets of final states as well as plant transition relations containing loops and uncontrollable events (e.g. failures). We report on experimental results on the use of our OSC synthesis algorithm to synthesize a C program implementing a minimum fuel OSC for two autonomous vehicles moving on a 4 x 4 grid.



Benedetto Intrigila, Ivano Salvo, and Stefano Sorgi. "A characterization of weakly ChurchRosser abstract reduction systems that are not ChurchRosser." Information and Computation 171, no. 2 (2001): 137–155. Academic Press, Inc.. ISSN: 08905401. DOI: 10.1006/inco.2001.2945.
Abstract: Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or ChurchRosser, CR) and weak confluence (or weak ChurchRosser, WCR) and their relationships can be studied in this setting: as a matter of fact, wellknown counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graphtheoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the NewmanÃ¢â‚¬â„¢s lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graphrewriting rules, with specific combinatorial properties.



Antonio Bucciarelli, Adolfo Piperno, and Ivano Salvo. "Intersection types and λdefinability." Mathematical Structures in Computer Science 13, no. 1 (2003): 15–53. Cambridge University Press. ISSN: 09601295. DOI: 10.1017/S0960129502003833.
Abstract: This paper presents a novel method for comparing computational properties of λterms that are typeable with intersection types, with respect to terms that are typeable with Curry types. We introduce a translation from intersection typing derivations to Curry typeable terms that is preserved by βreduction: this allows the simulation of a computation starting from a term typeable in the intersection discipline by means of a computation starting from a simply typeable term. Our approach proves strong normalisation for the intersection system naturally by means of purely syntactical techniques. The paper extends the results presented in Bucciarelli et al. (1999) to the whole intersection type system of Barendregt, Coppo and Dezani, thus providing a complete proof of the conjecture, proposed in Leivant (1990), that all functions uniformly definable using intersection types are already definable using Curry types.

