Efficient Symbolic Approaches for Quantitative Reactive Synthesis with Finite Tasks

This work introduces efficient symbolic algorithms for quantitative reactive synthesis. We consider resource-constrained robotic manipulators that need to interact with a human to achieve a complex task expressed in linear temporal logic. Our framework generates reactive strategies that not only guarantee task completion but also seek cooperation with the human when possible. We model the interaction as a two-player game and consider regret-minimizing strategies to encourage cooperation. We use symbolic representation of the game to enable scalability. For synthesis, we first introduce value iteration algorithms for such games with min-max objectives. Then, we extend our method to the regret-minimizing objectives. Our benchmarks reveal that our symbolic framework not only significantly improves computation time (up to an order of magnitude) but also can scale up to much larger instances of manipulation problems with up to 2x number of objects and locations than the state of the art.Comment: Submitted to IROS 202

Symbolic Search in Planning and General Game Playing

Search is an important topic in many areas of AI. Search problems often result in an immense number of states. This work addresses this by using a special datastructure, BDDs, which can represent large sets of states efficiently, often saving space compared to explicit representations. The first part is concerned with an analysis of the complexity of BDDs for some search problems, resulting in lower or upper bounds on BDD sizes for these. The second part is concerned with action planning, an area where the programmer does not know in advance what the search problem will look like. This part presents symbolic algorithms for finding optimal solutions for two different settings, classical and net-benefit planning, as well as several improvements to these algorithms. The resulting planner was able to win the International Planning Competition IPC 2008. The third part is concerned with general game playing, which is similar to planning in that the programmer does not know in advance what game will be played. This work proposes algorithms for instantiating the input and solving games symbolically. For playing, a hybrid player based on UCT and the solver is presented

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Verification of Branching-Time and Alternating-Time Properties for Exogenous Coordination Models

Information and communication systems enter an increasing number of areas of daily lives. Our reliance and dependence on the functioning of such systems is rapidly growing together with the costs and the impact of system failures. At the same time the complexity of hardware and software systems extends to new limits as modern hardware architectures become more and more parallel, dynamic and heterogenous. These trends demand for a closer integration of formal methods and system engineering to show the correctness of complex systems within the design phase of large projects. The goal of this thesis is to introduce a formal holistic approach for modeling, analysis and synthesis of parallel systems that potentially addresses complex system behavior at any layer of the hardware/software stack. Due to the complexity of modern hardware and software systems, we aim to have a hierarchical modeling framework that allows to specify the behavior of a parallel system at various levels of abstraction and that facilitates designing complex systems in an iterative refinement procedure, in which more detailed behavior is added successively to the system description. In this context, the major challenge is to provide modeling formalisms that are expressive enough to address all of the above issues and are at the same time amenable to the application of formal methods for proving that the system behavior conforms to its specification. In particular, we are interested in specification formalisms that allow to apply formal verification techniques such that the underlying model checking problems are still decidable within reasonable time and space bounds. The presented work relies on an exogenous modeling approach that allows a clear separation of coordination and computation and provides an operational semantic model where formal methods such as model checking are well suited and applicable. The channel-based exogenous coordination language Reo is used as modeling formalism as it supports hierarchical modeling in an iterative top-down refinement procedure. It facilitates reusability, exchangeability, and heterogeneity of components and forms the basis to apply formal verification methods. At the same time Reo has a clear formal semantics based on automata, which serve as foundation to apply formal methods such as model checking. In this thesis new modeling languages are presented that allow specifying complex systems in terms of Reo and automata models which yield the basis for a holistic approach on modeling, verification and synthesis of parallel systems. The second main contribution of this thesis are tailored branching-time and alternating time temporal logics as well as corresponding model checking algorithms. The thesis includes results on the theoretical complexity of the underlying model checking problems as well as practical results. For the latter the presented approach has been implemented in the symbolic verification tool set Vereofy. The implementation within Vereofy and evaluation of the branching-time and alternating-time model checker is the third main contribution of this thesis

Model checking and synthesis of best-effort strategies for safety and co-safety LTL

openThis thesis examines an optimality test algorithm to state whether the controller of a closed-loop system satisfies a formula in the best way with respect to an optimality principle. More formally, given a plant, a controller and a safety or co-safety \ltl formula, we want to figure out whether the formula is satisfied in the closed-loop between plant and controller and whether there exists another controller which does better than the given one according to an optimality principle. If such a controller exists, then it means that the given controller is not optimal and we provide the new controller just found as a proof of this fact. Otherwise, such a controller does not exist and it means that the given controller is optimal. To formally define the optimality principle, we introduce four semantics for both safety and co-safety fragments: bounded-value, best-effort, bounded-steps and As Soon As Possible (ASAP) semantics. The first semantics forces a state-sequence to satisfy a formula by keeping a plant variable always lower than a bound chosen a-priori, while the second semantics forces it to satisfy bounded-value a formula with the tightest possible bound. The third semantics forces a state-sequence to satisfy a formula in a maximum of steps chosen a-priori, while the last one forces it to satisfy a formula in as few steps as possible. Moreover, we prove that ASAP semantics is just one of the possible best-effort semantics instantiations. The optimality principle used during the thesis is the one given by the best-effort semantics since it is the most generic one. Afterwards, we show that this decision problem can be reduced to a synthesis problem where we try to synthesize a controller which is better than the given one by construction. Finally, we implement the optimality test algorithm in nuXmv and a custom safety and co-safety synthesizer from scratch, used by the algorithm to solve safety and reachability games.This thesis examines an optimality test algorithm to state whether the controller of a closed-loop system satisfies a formula in the best way with respect to an optimality principle. More formally, given a plant, a controller and a safety or co-safety \ltl formula, we want to figure out whether the formula is satisfied in the closed-loop between plant and controller and whether there exists another controller which does better than the given one according to an optimality principle. If such a controller exists, then it means that the given controller is not optimal and we provide the new controller just found as a proof of this fact. Otherwise, such a controller does not exist and it means that the given controller is optimal. To formally define the optimality principle, we introduce four semantics for both safety and co-safety fragments: bounded-value, best-effort, bounded-steps and As Soon As Possible (ASAP) semantics. The first semantics forces a state-sequence to satisfy a formula by keeping a plant variable always lower than a bound chosen a-priori, while the second semantics forces it to satisfy bounded-value a formula with the tightest possible bound. The third semantics forces a state-sequence to satisfy a formula in a maximum of steps chosen a-priori, while the last one forces it to satisfy a formula in as few steps as possible. Moreover, we prove that ASAP semantics is just one of the possible best-effort semantics instantiations. The optimality principle used during the thesis is the one given by the best-effort semantics since it is the most generic one. Afterwards, we show that this decision problem can be reduced to a synthesis problem where we try to synthesize a controller which is better than the given one by construction. Finally, we implement the optimality test algorithm in nuXmv and a custom safety and co-safety synthesizer from scratch, used by the algorithm to solve safety and reachability games

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

dtControl: Decision Tree Learning Algorithms for Controller Representation

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are smaller and more explainable. We present dtControl, an easily extensible tool for representing memoryless controllers as decision trees. We give a comprehensive evaluation of various decision tree learning algorithms applied to 10 case studies arising out of correct-by-construction controller synthesis. These algorithms include two new techniques, one for using arbitrary linear binary classifiers in the decision tree learning, and one novel approach for determinizing controllers during the decision tree construction. In particular the latter turns out to be extremely efficient, yielding decision trees with a single-digit number of decision nodes on 5 of the case studies

Symbolic Computation of Nonblocking Control Function for Timed Discrete Event Systems

In this paper, we symbolically compute a minimally restrictive nonblocking supervisor for timed discrete event systems, in the supervisory control theory context. The method is based on Timed Extended Finite Automata, which is an augmentation of extended finite automata (EFAs) by incorporating discrete time into the model. EFAs are ordinary automaton extended with discrete variables, guard expressions and action functions. To tackle large problems all computations are based on binary decision diagrams (BDDs). The main feature of this approach is that the BDD-based fixed-point computations is not based on “tick” models that have been commonly used in this area, leading to better performance in many cases. As a case study, we effectively computed the minimally restrictive nonblocking supervisor for a well-known production cell