Precedence Automata and Languages

Operator precedence grammars define a classical Boolean and deterministic context-free family (called Floyd languages or FLs). FLs have been shown to strictly include the well-known visibly pushdown languages, and enjoy the same nice closure properties. We introduce here Floyd automata, an equivalent operational formalism for defining FLs. This also permits to extend the class to deal with infinite strings to perform for instance model checking.Comment: Extended version of the paper which appeared in Proceedings of CSR 2011, Lecture Notes in Computer Science, vol. 6651, pp. 291-304, 2011. Theorem 1 has been corrected and a complete proof is given in Appendi

Deterministic recognizability of picture languages with Wang automata

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Application

Castle and Stairs to Learn Iteration: Co-Designing a UMC Learning Module with Teachers

This experience report presents a participatory process that involved primary school teachers and computer science education researchers. The objective of the process was to co-design a learning module to teach iteration to second graders using a visual programming environment and based on the Use-Modify-Create methodology. The co-designed learning module was piloted with three second-grade classes. We experienced that sharing and reconciling the different perspectives of researchers and teachers was doubly effective. On the one hand, it improved the quality of the resulting learning module; on the other hand, it constituted a very significant professional development opportunity for both teachers and researchers. We describe the co-designed learning module, discuss the most significant hinges in the process that led to such a product, and reflect on the lessons learned

Operator Precedence Languages: Their Automata-Theoretic and Logic Characterization

Operator precedence languages were introduced half a century ago by Robert Floyd to support deterministic and efficient parsing of context-free languages. Recently, we renewed our interest in this class of languages thanks to a few distinguishing properties that make them attractive for exploiting various modern technologies. Precisely, their local parsability enables parallel and incremental parsing, whereas their closure properties make them amenable to automatic verification techniques, including model checking. In this paper we provide a fairly complete theory of this class of languages: we introduce a class of automata with the same recognizing power as the generative power of their grammars; we provide a characterization of their sentences in terms of monadic second-order logic as has been done in previous literature for more restricted language classes such as regular, parenthesis, and input-driven ones; we investigate preserved and lost properties when extending the language sentences from finite length to infinite length ($omega$-languages). As a result, we obtain a class of languages that enjoys many of the nice properties of regular languages (closure and decidability properties, logic characterization) but is considerably larger than other families---typically parenthesis and input-driven ones---with the same properties, covering “almost” all deterministic languages

Toward a theory of input-driven locally parsable languages

If a context-free language enjoys the local parsability property then, no matter how the source string is segmented, each segment can be parsed independently, and an efficient parallel parsing algorithm becomes possible. The new class of locally chain parsable languages (LCPLs), included in the deterministic context-free language family, is here defined by means of the chain-driven automaton and characterized by decidable properties of grammar derivations. Such automaton decides whether to reduce or not a substring in a way purely driven by the terminal characters, thus extending the well-known concept of input-driven (ID) alias visibly pushdown machines. The LCPL family extends and improves the practically relevant Floyd's operator-precedence (OP) languages which are known to strictly include the ID languages, and for which a parallel-parser generator exists

Davinci Goes to Bebras: A Study on the Problem Solving Ability of GPT-3

In this paper we study the problem-solving ability of the Large Language Model known as GPT-3 (codename DaVinci), by considering its performance in solving tasks proposed in the “Bebras International Challenge on Informatics and Computational Thinking”. In our experiment, GPT-3 was able to answer with a majority of correct answers about one third of the Bebras tasks we submitted to it. The linguistic fluency of GPT-3 is impressive and, at a first reading, its explanations sound coherent, on-topic and authoritative; however the answers it produced are in fact erratic and the explanations often questionable or plainly wrong. The tasks in which the system performs better are those that describe a procedure, asking to execute it on a specific instance of the problem. Tasks solvable with simple, one-step deductive reasoning are more likely to obtain better answers and explanations. Synthesis tasks, or tasks that require a more complex logical consistency get the most incorrect answers

On the Maximum Coefficients of Rational Formal Series in Commuting Variables

Abstract. We study the maximum function of any R+-rational formal series S in two commuting variables, which assigns to every integer n ∈ N, the maximum coefficient of the monomials of degree n. We show that if S is a power of any primitive rational formal series, then its maximum function is of the order Θ(n k/2 λ n ) for some integer k ≥ −1 and some positive real λ. Our analysis is related to the study of limit distributions in pattern statistics. In particular, we prove a general criterion for establishing Gaussian local limit laws for sequences of discrete positive random variables