Search

This thesis examines Recursive Markov Chains (RMCs), their natural extensions and connection to other models. RMCs can model in a natural way probabilistic procedural programs and other systems that involve recursion and probability. An RMC is a set of ordinary finite state Markov Chains that are allowed to call each other recursively and it describes a potentially infinite, but countable, state ordinary Markov Chain. RMCs generalize in a precise sense several well studied probabilistic models in other domains such as natural language processing (Stochastic Context-Free Grammars), population dynamics (Multi-Type Branching Processes) and in queueing theory (Quasi-Birth-Death processes (QBDs)). In addition, RMCs can be extended to a controlled version called Recursive Markov Decision Processes (RMDPs) and also a game version referred to as Recursive (Simple) Stochastic Games (RSSGs). For analyzing RMCs, RMDPs, RSSGs we devised highly optimized numerical algorithms and implemented them in a tool called PReMo (Probabilistic Recursive Models analyzer). PReMo allows computation of the termination probability and expected termination time of RMCs and QBDs, and a restricted subset of RMDPs and RSSGs. The input models are described by the user in specifically designed simple input languages. Furthermore, in order to analyze the worst and best expected running time of probabilistic recursive programs we study models of RMDPs and RSSGs with positive rewards assigned to each of their transitions and provide new complexity upper and lower bounds of their analysis. We also establish some new connections between our models and models studied in queueing theory. Specifically, we show that (discrete time) QBDs can be described as a special subclass of RMCs and Tree-like QBDs, which are a generalization of QBDs, are equivalent to RMCs in a precise sense. We also prove that for a given QBD we can compute (in the unit cost RAM model) an approximation of its termination probabilities within i bits of precision in time polynomial in the size of the QBD and linear in i. Specifically, we show that we can do this using a decomposed Newton’s method.

We study cost optimisation in multi-mode systems with discrete costs. We first solve the problem in one dimension and next we study it in multiple dimensions. As a motivating example, we study the temperature control in buildings using heating, ventilation and air-conditioning system HVAC while paying the minimal cost as possible. By optimising the behaviour of the HVAC systems, lots of energy could be saved. We are interested in finding optimal solutions as well as approximate solutions with guarantees.

In this thesis, a number of search techniques are proposed as a solution for program and discrete controller synthesis (DCS). Classic synthesis techniques facilitate exhaus- tive search, while genetic programming has recently proven the potential of generic search techniques. But is genetic programming the right search technique for the synthesis prob- lem? In this thesis we challenge this belief and argue in favor of simulated annealing, a different class of general search techniques. We show that, in hindsight, the success of genetic programming has drawn from what is arguably a hybrid between simulated annealing and genetic programming, and compare the fitness of classic genetic program- ming, the hybrid form, and pure simulated annealing. Our experimental evaluation suggests that pure simulated annealing offers better results for automated programming than techniques based on genetic programming. Discrete Controller Synthesis (DCS) and Program Synthesis have similar goals: they are automated techniques to infer a control strategy and an implementation, respectively, that is correct by construction. We also investigate the application of the search tech- niques that we have been used for program synthesis for the computation of deterministic strategies solving symbolic Discrete Controller Synthesis (DCS) problems, where a model of the system under control is given along with desired objective behaviours. We experi- mentally confirm that relative performance results are similar to program synthesis, and give a complexity analysis of our simulated annealing algorithm for symbolic DCS. From the performance results we obtain, we draw the conclusion that simulated annealing, when combined with efficient model-checking techniques, is worth further investigating to solve symbolic DCS problems. A tool is designed to explore the parameter space of different synthesis techniques. Besides using it to synthesise a discrete control strategies for reactive systems (controller synthesis) and for protocol adapters for the coordination of different threads (software synthesis), we can also use it to study the influence of turning various screws in the syn- thesis process. For simulated annealing, PranCS allows the user to define the behaviour of the cooling schedule. For genetic programming, the user can select the population size.