Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)

The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without extra construction. An on-the-fly algorithm for the non-emptiness problem, using non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV 2010; Formal Methods in System Design, 201

Model Predictive Control for Signal Temporal Logic Specification

We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a receding horizon control framework. We prove correctness of our algorithms, and present experimental results for controller synthesis for building energy and climate control

Verifying safety and persistence in hybrid systems using flowpipes and continuous invariants

We describe a method for verifying the temporal property of persistence in non-linear hybrid systems. Given some system and an initial set of states, the method establishes that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flowpipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flowpipes or just reasoning about invariants alone can be insufficient and shows the richness of systems that one can handle with the proposed method, since the systems features modes with non-polynomial ODEs. We also propose an alternative method for proving persistence that relies solely on flowpipe computation

Taming Large Bounds in Synthesis from Bounded-Liveness Specifications

Automatic synthesis from temporal logic specifications is an attractive alternative to manual system design, due to its ability to generate correct-by-construction implementations from high-level specifications. Due to the high complexity of the synthesis problem, significant research efforts have been directed at developing practically efficient approaches for restricted specification language fragments. In this paper, we focus on the Safety LTL fragment of Linear Temporal Logic (LTL) syntactically extended with bounded temporal operators. We propose a new synthesis approach with the primary motivation to solve efficiently the synthesis problem for specifications with bounded temporal operators, in particular those with large bounds. The experimental evaluation of our method shows that for this type of specifications, it outperforms state-of-art synthesis tools, demonstrating that it is a promising approach to efficiently treating quantitative timing constraints in safety specifications

Towards budgeting in real-time calculus : deferrable servers

Budgeting of resources is an often used solution for guaranteeing performance of lower priority tasks. In this paper, we take a formal approach to the modeling of a deferrable server budgeting strategy, using real-time calculus. We prove a scheduling theorem for deferrable servers, and as a corollary show that an earlier claim of Davis and Burns, that periodic servers dominate deferrable servers with respect to schedulability, no longer holds when the context of the comparison is slightly generalized

Computational Modeling of Complex Protein Activity Networks

Because of the numerous entities interacting, the complexity of the networks that regulate cell fate makes it impossible to analyze and understand them using the human brain alone. Computational modeling is a powerful method to unravel complex systems. We recently described the development of a user-friendly computational tool, Analysis of Networks with Interactive MOdeling (ANIMO). ANIMO is a powerful tool to formalize knowledge on molecular interactions. This formalization entails giving a precise mathematical (formal) description of molecular states and of interactions between molecules. Such a model can be simulated, thereby in silico mimicking the processes that take place in the cell. In sharp contrast to classical graphical representations of molecular interaction networks, formal models allow in silico experiments and functional analysis of the dynamic behavior of the network. In addition, ANIMO was developed specifically for use by biologists who have little or no prior modeling experience. In this chapter, we guide the reader through the ANIMO workflow using osteoarthritis (OA) as a case study. WNT, IL-1β, and BMP signaling and cross talk are used as a concrete and illustrative model

Behavioural Preorders on Stochastic Systems - Logical, Topological, and Computational Aspects

Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly. However, it is a notoriously difficult task to ensure that the software running on computers behaves correctly. One approach to ease this task is that of model checking, where a model of the system is made using some mathematical formalism. Requirements expressed in a formal language can then be verified against the model in order to give guarantees that the model satisfies the requirements. For many computer systems, time is an important factor. As such, we need our formalisms and requirement languages to be able to incorporate real time. We therefore develop formalisms and algorithms that allow us to compare and express properties about real-time systems. We first introduce a logical formalism for reasoning about upper and lower bounds on time, and study the properties of this formalism, including axiomatisation and algorithms for checking when a formula is satisfied. We then consider the question of when a system is faster than another system. We show that this is a difficult question which can not be answered in general, but we identify special cases where this question can be answered. We also show that under this notion of faster-than, a local increase in speed may lead to a global decrease in speed, and we take step towards avoiding this. Finally, we consider how to compare the real-time behaviour of systems not just qualitatively, but also quantitatively. Thus, we are interested in knowing how much one system is faster or slower than another system. This is done by introducing a distance between systems. We show how to compute this distance and that it behaves well with respect to certain properties.Comment: PhD dissertation from Aalborg Universit