Learning probability distributions generated by finite-state machines

We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft

Certified Reinforcement Learning with Logic Guidance

This paper proposes the first model-free Reinforcement Learning (RL) framework to synthesise policies for unknown, and continuous-state Markov Decision Processes (MDPs), such that a given linear temporal property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), namely a finite-state machine expressing the property. Exploiting the structure of the LDBA, we shape a synchronous reward function on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces that probabilistically satisfy the linear temporal property. This probability (certificate) is also calculated in parallel with policy learning when the state space of the MDP is finite: as such, the RL algorithm produces a policy that is certified with respect to the property. Under the assumption of finite state space, theoretical guarantees are provided on the convergence of the RL algorithm to an optimal policy, maximising the above probability. We also show that our method produces ''best available'' control policies when the logical property cannot be satisfied. In the general case of a continuous state space, we propose a neural network architecture for RL and we empirically show that the algorithm finds satisfying policies, if there exist such policies. The performance of the proposed framework is evaluated via a set of numerical examples and benchmarks, where we observe an improvement of one order of magnitude in the number of iterations required for the policy synthesis, compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782

Learning deterministic probabilistic automata from a model checking perspective

Probabilistic automata models play an important role in the formal design and analysis of hard- and software systems. In this area of applications, one is often interested in formal model-checking procedures for verifying critical system properties. Since adequate system models are often difficult to design manually, we are interested in learning models from observed system behaviors. To this end we adopt techniques for learning finite probabilistic automata, notably the Alergia algorithm. In this paper we show how to extend the basic algorithm to also learn automata models for both reactive and timed systems. A key question of our investigation is to what extent one can expect a learned model to be a good approximation for the kind of probabilistic properties one wants to verify by model checking. We establish theoretical convergence properties for the learning algorithm as well as for probability estimates of system properties expressed in linear time temporal logic and linear continuous stochastic logic. We empirically compare the learning algorithm with statistical model checking and demonstrate the feasibility of the approach for practical system verification

Bootstrapping and learning PDFA in data streams

Best Student Paper ICGI 2012Markovian models with hidden state are widely-used formalisms for modeling sequential phenomena. Learnability of these models has been well studied when the sample is given in batch mode, and algorithms with PAC-like learning guarantees exist for specic classes of models such as Probabilistic Deterministic Finite Automata (PDFA). Here we focus on PDFA and give an algorithm for infering models in this class under the stringent data stream scenario: unlike existing methods, our algorithm works incrementally and in one pass, uses memory sublinear in the stream length, and processes input items in amortized constant time. We provide rigorous PAC-like bounds for all of the above, as well as an evaluation on synthetic data showing that the algorithm performs well in practice. Our algorithm makes a key usage of several old and new sketching techniques. In particular, we develop a new sketch for implementing bootstrapping in a streaming setting which may be of independent interest. In experiments we have observed that this sketch yields important reductions in the examples required for performing some crucial statistical tests in our algorithm.Peer ReviewedAward-winningPostprint (published version

Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges

In recent years, formal methods have been extensively used in the design of autonomous systems. By employing mathematically rigorous techniques, formal methods can provide fully automated reasoning processes with provable safety guarantees for complex dynamic systems with intricate interactions between continuous dynamics and discrete logics. This paper provides a comprehensive review of formal controller synthesis techniques for safety-critical autonomous systems. Specifically, we categorize the formal control synthesis problem based on diverse system models, encompassing deterministic, non-deterministic, and stochastic, and various formal safety-critical specifications involving logic, real-time, and real-valued domains. The review covers fundamental formal control synthesis techniques, including abstraction-based approaches and abstraction-free methods. We explore the integration of data-driven synthesis approaches in formal control synthesis. Furthermore, we review formal techniques tailored for multi-agent systems (MAS), with a specific focus on various approaches to address the scalability challenges in large-scale systems. Finally, we discuss some recent trends and highlight research challenges in this area

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

Learning discrete Hidden Markov Models from state distribution vectors

Hidden Markov Models (HMMs) are probabilistic models that have been widely applied to a number of fields since their inception in the late 1960’s. Computational Biology, Image Processing, and Signal Processing, are but a few of the application areas of HMMs. In this dissertation, we develop several new efficient learning algorithms for learning HMM parameters. First, we propose a new polynomial-time algorithm for supervised learning of the parameters of a first order HMM from a state probability distribution (SD) oracle. The SD oracle provides the learner with the state distribution vector corresponding to a query string. We prove the correctness of the algorithm and establish the conditions under which it is guaranteed to construct a model that exactly matches the oracle’s target HMM. We also conduct a simulation experiment to test the viability of the algorithm. Furthermore, the SD oracle is proven to be necessary for polynomial-time learning in the sense that the consistency problem for HMMs, where a training set of state distribution vectors such as those provided by the SD oracle is used but without the ability to query on arbitrary strings, is NP-complete. Next, we define helpful distributions on an instance set of strings for which polynomial-time HMM learning from state distribution vectors is feasible in the absence of an SD oracle and propose a new PAC-learning algorithm under helpful distribution for HMM parameters. The PAC-learning algorithm ensures with high probability that HMM parameters can be learned from training examples without asking queries. Furthermore, we propose a hybrid learning algorithm for approximating HMM parameters from a dataset composed of strings and their corresponding state distribution vectors, and provide supporting experimental data, which indicates our hybrid algorithm produces more accurate approximations than the existing method

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic