Improved set-based symbolic algorithms for parity games

Graph games with omega-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and the verification of branching time properties). Parity conditions are canonical forms to specify omega-regular winning conditions. Graph games with parity conditions are equivalent to mu-calculus model checking, and thus a very important algorithmic problem. Symbolic algorithms are of great significance because they provide scalable algorithms for the analysis of large finite-state systems, as well as algorithms for the analysis of infinite-state systems with finite quotient. A set-based symbolic algorithm uses the basic set operations and the one-step predecessor operators. We consider graph games with n vertices and parity conditions with c priorities (equivalently, a mu-calculus formula with c alternations of least and greatest fixed points). While many explicit algorithms exist for graph games with parity conditions, for set-based symbolic algorithms there are only two algorithms (notice that we use space to refer to the number of sets stored by a symbolic algorithm): (a) the basic algorithm that requires O(n^c) symbolic operations and linear space; and (b) an improved algorithm that requires O(n^{c/2+1}) symbolic operations but also O(n^{c/2+1}) space (i.e., exponential space). In this work we present two set-based symbolic algorithms for parity games: (a) our first algorithm requires O(n^{c/2+1}) symbolic operations and only requires linear space; and (b) developing on our first algorithm, we present an algorithm that requires O(n^{c/3+1}) symbolic operations and only linear space. We also present the first linear space set-based symbolic algorithm for parity games that requires at most a sub-exponential number of symbolic operations

Generalization Strategies for the Verification of Infinite State Systems

We present a method for the automated verification of temporal properties of infinite state systems. Our verification method is based on the specialization of constraint logic programs (CLP) and works in two phases: (1) in the first phase, a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase, the specialized program is evaluated by using a bottom-up strategy. The effectiveness of the method strongly depends on the generalization strategy which is applied during the program specialization phase. We consider several generalization strategies obtained by combining techniques already known in the field of program analysis and program transformation, and we also introduce some new strategies. Then, through many verification experiments, we evaluate the effectiveness of the generalization strategies we have considered. Finally, we compare the implementation of our specialization-based verification method to other constraint-based model checking tools. The experimental results show that our method is competitive with the methods used by those other tools. To appear in Theory and Practice of Logic Programming (TPLP).Comment: 24 pages, 2 figures, 5 table

Infinite/infinite analysis as a tool for an early oriented synthesis of a reactive pressure swing distillation

The study contributes to the characterization of an original reactive pressure swing distillation system. The methyl acetate (MeAc) transesterification with ethanol (EtOH) to produce methanol (MeOH) and ethyl acetate (EtAc) is shown as illustrative example. The streams outside the units are evaluated by the ∞/∞ analysis to provide insights on the process behavior. Two simpler systems with recycling stream are also presented.The ∞/∞ analysis allows checking the interrelation of the system streams without any column design consideration. Unfeasible regions, low limit values, multiplicity regions, discontinuities, control difficulties, recommendable operation conditions and column profile combinations are predicted and discussed. All these information are useful to establish an early and suitable system design strategy

Learning-Based Synthesis of Safety Controllers

We propose a machine learning framework to synthesize reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration, two-player games over (potentially) infinite graphs. Our framework targets safety games with infinitely many vertices, but it is also applicable to safety games over finite graphs whose size is too prohibitive for conventional synthesis techniques. The learning takes place in a feedback loop between a teacher component, which can reason symbolically about the safety game, and a learning algorithm, which successively learns an overapproximation of the winning region from various kinds of examples provided by the teacher. We develop a novel decision tree learning algorithm for this setting and show that our algorithm is guaranteed to converge to a reactive safety controller if a suitable overapproximation of the winning region can be expressed as a decision tree. Finally, we empirically compare the performance of a prototype implementation to existing approaches, which are based on constraint solving and automata learning, respectively

Preliminary Design of Reactive Distillation Columns

A procedure that combines feasibility analysis, synthesis and design of reactive distillation columns is introduced. The main interest of this methodology lies on a progressive introduction of the process complexity. From minimal information concerning the physicochemical properties of the system, three steps lead to the design of the unit and the specification of its operating conditions. Most of the methodology exploits and enriches approaches found in the literature. Each step is described and our contribution is underlined. Its application is currently limited to equilibrium reactive systems where degree of freedom is equal to 2 or less than 2. This methodology which provides a reliable initialization point for the optimization of the process has been applied with success to different synthesis. The production of methyl-tert-butyl-ether (MTBE) and methyl acetate are presented as examples

On the Executability of Interactive Computation

The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are reactively executable. In this article we provide a comparison of the two models. We show, on the one hand, that the behaviour exhibited by ITMs is reactively executable, and, on the other hand, that the stream translations naturally associated with RTMs are interactively computable. We conclude from these results that the theory of reactive executability subsumes the theory of interactive computability. Inspired by the existing model of ITMs with advice, which provides a model of evolving computation, we also consider RTMs with advice and we establish that a facility of advice considerably upgrades the behavioural expressiveness of RTMs: every countable transition system can be simulated by some RTM with advice up to a fine notion of behavioural equivalence.Comment: 15 pages, 0 figure