Related papers: State Complexity of Projection on Languages Recogn…
We describe a framework for using natural language to design state abstractions for imitation learning. Generalizable policy learning in high-dimensional observation spaces is facilitated by well-designed state representations, which can…
Studying language models (LMs) in terms of well-understood formalisms allows us to precisely characterize their abilities and limitations. Previous work has investigated the representational capacity of recurrent neural network (RNN) LMs in…
A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language…
We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game…
The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an…
We examine the complexity of basic regular operations on languages represented by Boolean and alternating finite automata. We get tight upper bounds m+n and m+n+1 for union, intersection, and difference, 2^m+n and 2^m+n+1 for concatenation,…
An automaton is synchronizing if there is a word that maps all states onto the same state. \v{C}ern\'{y}'s conjecture on the length of the shortest such word is probably the most famous open problem in automata theory. We consider the…
Register automata are finite automata equipped with a finite set of registers ranging over the domain of some relational structure like $(\mathbb N;=)$ or $(\mathbb Q;<)$. Register automata process words over the domain, and along a run of…
We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the…
We determine the accepting-state spectrum of reversal for permutation automata exactly, thereby proving the Rauch--Holzer conjecture on this operation. For every $m \ge 2$ and every $\alpha \ge 2$, we construct a binary permutation…
We study the recognition of R-trivial idempotent (R1) languages by various models of "decide-and-halt" quantum finite automata (QFA) and probabilistic reversible automata (DH-PRA). We introduce bistochastic QFA (MM-BQFA), a model which…
We show that the minimization of visibly pushdown automata is NP-complete. This result is obtained by introducing immersions, that recognize multiple languages (over a usual, non-visible alphabet) using a common deterministic transition…
We report on simulation, hierarchy, and decidability results for Practical Regular Expressions (PRE), which may include back references in addition to the standard operations union, concatenation, and star. The following results are…
I study the state complexity of binary operations on regular languages over different alphabets. It is well known that if $L'_m$ and $L_n$ are languages restricted to be over the same alphabet, with $m$ and $n$ quotients, respectively, the…
In this paper, we introduce a new model of deterministic Watson-Crick automaton namely restricted deterministic Watson- Crick automaton which is a deterministic Watson-Crick automaton where the complementarity string in the lower strand is…
Context free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these…
The problem DFA-Intersection-Nonemptiness asks if a given number of deterministic automata accept a common word. In general, this problem is PSPACE-complete. Here, we investigate this problem for the subclasses of commutative automata and…
1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…