Vadim Alimguzhin, Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. On Model Based Synthesis of Embedded Control Software. Vol. abs/1207.4474. CoRR, Technical Report, 2012.
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 AnalogtoDigital (AD) conversion) correctbyconstruction 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 setup 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 nonfunctional requirements (such us optimal setup time, ripple) with software nonfunctional 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.

Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. Model Based Synthesis of Control Software from System Level Formal Specifications. Vol. abs/1107.5638. CoRR, Technical Report, 2013.
Abstract: Many Embedded Systems are indeed Software Based Control Systems, 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 automatic synthesis of embedded systems control software.
We present an algorithm, along with a tool QKS implementing it, that from a formal model (as a Discrete Time Linear Hybrid System) of the controlled system (plant), implementation specifications (that is, number of bits in the AnalogtoDigital, AD, conversion) and System Level Formal Specifications (that is, safety and liveness requirements for the closed loop system) returns correctbyconstruction control software that has a Worst Case Execution Time (WCET) linear in the number of AD bits and meets the given specifications.
We show feasibility of our approach by presenting experimental results on using it to synthesize control software for a buck DCDC converter, a widely used mixedmode analog circuit, and for the inverted pendulum.

Vadim Alimguzhin, Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. Automatic Control Software Synthesis for Quantized Discrete Time Hybrid Systems. Vol. abs/1207.4098. CoRR, Technical Report, 2012.
Abstract: Many Embedded Systems are indeed Software Based Control Systems, 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 automatic synthesis of embedded systems control software. This paper addresses control software synthesis for discrete time nonlinear systems. We present a methodology to overapproximate the dynamics of a discrete time nonlinear hybrid system H by means of a discrete time linear hybrid system L(H), in such a way that controllers for L(H) are guaranteed to be controllers for H. We present experimental results on the inverted pendulum, a challenging and meaningful benchmark in nonlinear Hybrid Systems control.

Federico Mari, and Enrico Tronci. "CEGAR Based Bounded Model Checking of Discrete Time Hybrid Systems." In Hybrid Systems: Computation and Control (HSCC 2007), edited by A. Bemporad, A. Bicchi and G. C. Buttazzo, 399–412. Lecture Notes in Computer Science 4416. Springer, 2007. DOI: 10.1007/9783540714934_32.
Abstract: Many hybrid systems can be conveniently modeled as Piecewise Affine Discrete Time Hybrid Systems PADTHS. As well known Bounded Model Checking (BMC) for such systems comes down to solve a Mixed Integer Linear Programming (MILP) feasibility problem. We present a SAT based BMC algorithm for automatic verification of PADTHSs. Using Counterexample Guided Abstraction Refinement (CEGAR) our algorithm gradually transforms a PADTHS verification problem into larger and larger SAT problems. Our experimental results show that our approach can handle PADTHSs that are more then 50 times larger than those that can be handled using a MILP solver.
Keywords: Model Checking, Abstraction, CEGAR, SAT, Hybrid Systems, DTHS

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.

Giuseppe Della Penna, Benedetto Intrigila, Igor Melatti, Enrico Tronci, and Marisa Venturini Zilli. "Finite Horizon Analysis of Stochastic Systems with the Mur$\varphi$ Verifier." In Theoretical Computer Science, 8th Italian Conference, ICTCS 2003, Bertinoro, Italy, October 1315, 2003, Proceedings, edited by C. Blundo and C. Laneve, 58–71. Lecture Notes in Computer Science 2841. Springer, 2003. ISSN: 3540202161. DOI: 10.1007/9783540452089_6.
Abstract: Many reactive systems are actually Stochastic Processes. Automatic analysis of such systems is usually very difficult thus typically one simplifies the analysis task by using simulation or by working on a simplified model (e.g. a Markov Chain). We present a Finite Horizon Probabilistic Model Checking approach which essentially can handle the same class of stochastic processes of a typical simulator. This yields easy modeling of the system to be analyzed together with formal verification capabilities. Our approach is based on a suitable disk based extension of the Mur$\varphi$ verifier. Moreover we present experimental results showing effectiveness of our approach.

Enrico Tronci. "Automatic Synthesis of Controllers from Formal Specifications." In Proc of 2nd IEEE International Conference on Formal Engineering Methods (ICFEM), 134–143. Brisbane, Queensland, Australia, 1998. DOI: 10.1109/ICFEM.1998.730577.
Abstract: Many safety critical reactive systems are indeed embedded control systems. Usually a control system can be partitioned into two main subsystems: a controller and a plant. Roughly speaking: the controller observes the state of the plant and sends commands (stimulus) to the plant to achieve predefined goals. We show that when the plant can be modeled as a deterministic finite state system (FSS) it is possible to effectively use formal methods to automatically synthesize the program implementing the controller from the plant model and the given formal specifications for the closed loop system (plant+controller). This guarantees that the controller program is correct by construction. To the best of our knowledge there is no previously published effective algorithm to extract executable code for the controller from closed loop formal specifications. We show practical usefulness of our techniques by giving experimental results on their use to synthesize C programs implementing optimal controllers (OCs) for plants with more than 109 states.

Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. "Synthesizing Control Software from Boolean Relations." International Journal on Advances in Software vol. 5, nr 3&4 (2012): 212–223. IARIA. ISSN: 19422628.
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 worst case execution time
linear in nr, being n = x the number of
input arguments for functions in F and r the
number of functions in F. Moreover, a formal
proof of the proposed algorithm correctness is
also shown. Finally, we present experimental
results showing effectiveness of the proposed
algorithm.
Keywords: Control Software Synthesis; Embedded Systems; Model Checking

Federico Mari, Igor Melatti, Ivano Salvo, and Enrico Tronci. "From Boolean Relations to Control Software." In Proceedings of ICSEA 2011, The Sixth International Conference on Software Engineering Advances, 528–533. ThinkMind, 2011. ISSN: 9781612081656. Notes: Best Paper Award.
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) linear in nr, being n = x the number of input arguments for functions in F and r the number of functions in F.
