Formal Languages and Automata Theory Papers of the Week

Under uniform transmission, we determine the received binary words that maximize input entropy for two-deletion and two-insertion channels.

Given a uniformly bounded number of distinct examples from an unknown target language, a generator must produce infinitely many new examples from that language with probability one while protecting the privacy of its input. We introduce a new combinatorial dimension termed the nested branching dimension and prove that a language class is privately uniformly generatable if and only if both its closure dimension and nested branching dimension are finite.

To find a subclass of VASS in which the problem has lower complexity we define alphabetically bidirected VASS as ones where bidirectedness is also visible in the input letters.

A reversible Turing machine (RTM) is a Turing machine in which every instantaneous description has at most one predecessor. Writing URTM(m,n) for a universal RTM with m states and n symbols, we construct URTM(3,600), URTM(4,41), URTM(5,37), URTM(6,30), URTM(7,28), URTM(8,21), and URTM(85,2); each of them has fewer states or fewer symbols than each of the nine URTMs in Morita's book (2017).

We study distributed synthesis for two processes communicating in rounds over unreliable links, with at least one message delivered in every round.

The definition of Leibnizian strings are rather quite non-linear and for that purpose we classify non-Leibnizian strings for which there is a simpler criterion on maximal neighborhoods of characters.

We study weighted grammars and finite automata whose weights are scalar grade-reliability pairs inspired by Z-numbers.

We study the scope grammar, a deliberately ambiguous context-free grammar whose derivation trees are the readings of a connective skeleton and whose quotient by logical equivalence is what matters downstream.

We prove that, whenever the literal decoder of $C$ is synchronizing, it has a reset word of length at most $(k-1)(4k-5)$.

Weighted automata learning has been well-studied over (semi)rings which have a dimension theory. In this work, we investigate active learning for weighted automata over semirings that lack such a structure.

This study proposes a set-theoretic model for quantitatively measuring the completeness of a learning resource with respect to a course syllabus.

We construct a functor $F$ from $\mathbf{Grp}$, the category of groups (or any similar algebraic structure), to the category of pointed digraphs, and show its faithfulness. We introduce the image category $\mathcal C_{n,\phi}$ of state transition graphs of all such group-alphabet cellular automata, and show $F$ is an equivalence onto this category.

Our main technical contribution is a characterization of the sublinear class in terms of algebra, word congruences, regular expressions, and logic.