Related papers: Complexity of Problems for Commutative Grammars
We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…
We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove…
We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for…
It has been conjectured that the Parikh (commutative) image of every language over an infinite alphabet recognized by an automaton with registers is defined by a rational expression. This conjecture is known to hold for all languages…
We show that the Parikh image of the language of an NFA with n states over an alphabet of size k can be described as a finite union of linear sets with at most k generators and total size 2^{O(k^2 log n)}, i.e., polynomial for all fixed k…
Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run, thereby preserving many of the desirable algorithmic properties of finite automata. Here, we study the…
Parikh's theorem states that every Context Free Language (CFL) has the same Parikh image as that of a regular language. A finite state automaton accepting such a regular language is called a Parikh-equivalent automaton. In the worst case,…
This paper investigates complexity of the uniform membership problem for hyperedge replacement grammars in comparison with other mildly context-sensitive grammar formalisms. It turns out that the complexity of this problem depends on how…
We study Parikh automata on finite and infinite words. First we establish some results for Parikh automata on finite words. Following, we present several definitions of Parikh automata on infinite words. We consider the deterministic as…
Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference DLT-WORDS 2023 we showed that fixed points of…
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a…
We show that the language equivalence problem for regular and context-free commutative grammars is coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equivalence problems for…
We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them. Those grammars can alternatively be viewed as an…
The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton's method to…
Parikh's Theorem is a fundamental result in automata theory with numerous applications in computer science: software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic…
Indexed languages are a classical notion in formal language theory. As the language equivalent of second-order pushdown automata, they have received considerable attention in higher-order model checking. Unfortunately, counting properties…
We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L(A): its…
We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…
We study algorithmic complexity and expressive power of fusion grammars, a novel formalism introduced in [Kreowski, Kuske, and Lye 2017], which extends hyperedge replacement grammars. In the first part of the work, we prove that the…
We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for strict and non-strict cut-points of polynomially ambiguous…