Abstract: In the type frame originating from the flat domain of boolean values, we single out elements which are hereditarily total. We show that these elements can be defined, up to total equivalence, by sequential programs. The elements of an equivalence class of the totality equivalence relation (totality class) can be seen as different algorithms for computing a given set-theoretic boolean function. We show that the bottom element of a totality class, which is sequential, corresponds to the most eager algorithm, and the top to the laziest one. Finally we suggest a link between size of totality classes and a well known measure of complexity of boolean functions, namely their sensitivity.

Abstract: CuCh machine extends pure lambda–calculus with algebraic data types and provides a the possibility of defining functions over the disjoint sum of algebras. We exploit such natural form of overloading to define a functional interpretation of a simple, but significant fragment of a typical object-oriented language.

Abstract: We present an ambient-like calculus in which the open capability is dropped, and a new form of “lightweight� process mobility is introduced. The calculus comes equipped with a type system that allows the kind of values exchanged in communications and the access and mobility properties of processes to be controlled. A type inference procedure determines the “minimal� requirements to accept a system or a component as well typed. This gives a kind of principal typing. As an expressiveness test, we show that some well known calculi of concurrency and mobility can be encoded in our calculus in a natural way.

Abstract: Many Embedded Systems are indeed Software Based Control Systems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for control software. Given the formal model of a plant as a Discrete Time Linear Hybrid System and the implementation specifications (that is, number of bits in the Analog-to-Digital (AD) conversion) correct-by-construction control software can be automatically generated from System Level Formal Specifications of the closed loop system (that is, safety and liveness requirements), by computing a suitable finite abstraction of the plant.
With respect to given implementation specifications, the automatically generated code implements a time optimal control strategy (in terms of set-up time), has a Worst Case Execution Time linear in the number of AD bits $b$, but unfortunately, its size grows exponentially with respect to $b$. In many embedded systems, there are severe restrictions on the computational resources (such as memory or computational power) available to microcontroller devices.
This paper addresses model based synthesis of control software by trading system level non-functional requirements (such us optimal set-up time, ripple) with software non-functional requirements (its footprint). Our experimental results show the effectiveness of our approach: for the inverted pendulum benchmark, by using a quantization schema with 12 bits, the size of the small controller is less than 6% of the size of the time optimal one.

Abstract: Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware) synthesis process is finding effective solutions to the functional equation defined by K. This entails finding a (set of) boolean function(s) F (typically represented using OBDDs, Ordered Binary Decision Diagrams) such that: 1) for all x for which K is satisfiable, K(x, F(x)) = 1 holds; 2) the implementation of F is efficient with respect to given implementation parameters such as code size or execution time. While this problem has been widely studied in digital hardware synthesis, little has been done in a software synthesis context. Unfortunately the approaches developed for hardware synthesis cannot be directly used in a software context. This motivates investigation of effective methods to solve the above problem when F has to be implemented with software. In this paper we present an algorithm that, from an OBDD representation for K, generates a C code implementation for F that has the same size as the OBDD for F and a WCET (Worst Case Execution Time) at most O(nr), being n = |x| the number of arguments of functions in F and r the number of functions in F.