Scalable Anytime Algorithms for Learning Fragments

International audienceAbstract Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning formulas in fragments of LTL without the $$\mathbf {U}$$ U -operator for classifying traces; despite a growing interest of the research community, existing solutions suffer from two limitations: they do not scale beyond small formulas, and they may exhaust computational resources without returning any result. We introduce a new algorithm addressing both issues: our algorithm is able to construct formulas an order of magnitude larger than previous methods, and it is anytime, meaning that it in most cases successfully outputs a formula, albeit possibly not of minimal size. We evaluate the performances of our algorithm using an open source implementation against publicly available benchmarks

The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes

We study the never-worse relation (NWR) for Markov decision processes with an infinite-horizon reachability objective. A state q is never worse than a state p if the maximal probability of reaching the target set of states from p is at most the same value from q, regard- less of the probabilities labelling the transitions. Extremal-probability states, end components, and essential states are all special cases of the equivalence relation induced by the NWR. Using the NWR, states in the same equivalence class can be collapsed. Then, actions leading to sub- optimal states can be removed. We show the natural decision problem associated to computing the NWR is coNP-complete. Finally, we ex- tend a previously known incomplete polynomial-time iterative algorithm to under-approximate the NWR

Statistical comparison of algorithm performance through instance selection

Algorithms and the Foundations of Software technolog

Alternating Tree Automata with Qualitative Semantics

We study alternating automata with qualitative semantics over infinite binary trees: Alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this article, we prove a positive and a negative result for the emptiness problem of alternating automata with qualitative semantics. The positive result is the decidability of the emptiness problem for the case of Büchi acceptance condition. An interesting aspect of our approach is that we do not extend the classical solution for solving the emptiness problem of alternating automata, which first constructs an equivalent non-deterministic automaton. Instead, we directly construct an emptiness game making use of imperfect information. The negative result is the undecidability of the emptiness problem for the case of co-Büchi acceptance condition. This result has two direct consequences: The undecidability of monadic second-order logic extended with the qualitative path-measure quantifier and the undecidability of the emptiness problem for alternating tree automata with non-zero semantics, a recently introduced probabilistic model of alternating tree automata

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Reconhecimento antecipado de problemas ortográficos em escreventes novatos: quando e como acontecem

A aprendizagem da ortográfica constitui um processo complexo, envolvendo questões lexicais e gramaticais. Muitos estudos sobre essa aprendizagem tratam os problemas ortográficos de modo independente e separado da produção textual. Neste estudo defendemos a importância de se analisar a aprendizagem da ortografia a partir da perspectiva proposta pela Genética Textual, colocando em destaque a gênese do processo de escritura e criação textual. Apresentamos o Sistema Ramos, metodologia de investigação que registra o processo de escritura em tempo e espaço real da sala de aula. Esse Sistema oferece informações multimodais (fala, escrita, gestualidade) sobre o que alunos, em duplas, reconhecem como problemas ortográficos (PO) e os comentários espontâneos feitos quando estão escrevendo o texto. Este estudo analisa justamente o momento em que aconteceram esses reconhecimentos e os comentários de duas alunas no 2º ano de escolaridade, durante a produção de seis histórias inventadas. Mais do que uma análise quantitativa dos tipos de PO identificados no produto, apresentamos uma análise enunciativa e microgenética de reconhecimentos de PO e seus comentários, particularmente aqueles PO antecipados pelas escreventes. Os resultados indicam: i. Reconhecimentos ensejam comentários nem sempre relacionados ao PO identificado; ii. Reconhecimentos e comentários estão relacionados aos conteúdos ortográficos ensinados em sala de aula; iii. Alguns PO reconhecidos envolvem a articulação de diferentes níveis linguísticos. Esses aspectos podem contribuir para a compreensão da aprendizagem da ortografia em situações didáticas propiciadas pela escrita colaborativa a dois.The acquisition of spelling competence is a complex process, involving lexical and grammatical questions. Research, however, almost always places the spelling from an autonomous point of view and disconnected from the other components of writing. In this text, we present the relevance of the Ramos System that captures students in an ecological situation of text production in pairs, allowing access to the processes for solving orthographic problems. Collaborative writing also grants access to comments made by students during the process of textual linearization. Our study focuses on the recognition of spelling problems (SP) and the comments made regarding such problems by two 2nd grade students during the production of six invented stories. More than a quantitative analysis of the types of SP identified in the product, we were interested in making a qualitative and fine analysis of oral recognitions of SP, particularly those SP anticipated by the writers. Our results indicate that: i. Recognition motivates comments that are not always related to the identified SP; ii. Recognition and comments are related to the orthographic contents taught in the classroom; iii. Some of the recognized SP involve the articulation between different linguistic levels. These aspects can contribute for the comprehension of orthographic learning in didactic situations provided by collaborative writing.publishe

Probabilistic automata of bounded ambiguity

Probabilistic automata are a computational model introduced by Michael Rabin, extending nondeterministic finite automata with probabilistic transitions. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are undecidable. In this work we focus on the emptiness problem, which asks whether a given probabilistic automaton accepts some word with probability higher than a given threshold. We consider a natural and well-studied structural restriction on automata, namely the degree of ambiguity, which is defined as the maximum number of accepting runs over all words. We observe that undecidability of the emptiness problem requires infinite ambiguity and so we focus on the case of finitely ambiguous probabilistic automata. Our main results are to construct efficient algorithms for analysing finitely ambiguous probabilistic automata through a reduction to a multi-objective optimisation problem, called the stochastic path problem. We obtain a polynomial time algorithm for approximating the value of finitely ambiguous probabilistic automata and a quasi-polynomial time algorithm for the emptiness problem for 2-ambiguous probabilistic automata

Trace refinement in labelled Markov decision processes

Given two labelled Markov decision processes (MDPs), the trace-refinement problem asks whether for all strategies of the first MDP there exists a strategy of the second MDP such that the induced labelled Markov chains are trace-equivalent. We show that this problem is decidable in polynomial time if the second MDP is a Markov chain. The algorithm is based on new results on a particular notion of bisimulation between distributions over the states. However, we show that the general trace-refinement problem is undecidable, even if the first MDP is a Markov chain. Decidability of those problems was stated as open in 2008. We further study the decidability and complexity of the trace-refinement problem provided that the strategies are restricted to be memoryless