scholarly journals Lower Bounds on the State Complexity of Population Protocols

2021 ◽  
Author(s):  
Philipp Czerner ◽  
Javier Esparza
Keyword(s):  
Lower Bounds ◽  
The State ◽  
State Complexity ◽  
Population Protocols

scholarly journals STATE COMPLEXITY AND THE MONOID OF TRANSFORMATIONS OF A FINITE SET

2005 ◽  
Vol 16 (03) ◽  
pp. 547-563 ◽  
Author(s):  
BRYAN KRAWETZ ◽  
JOHN LAWRENCE ◽  
JEFFREY SHALLIT
Keyword(s):  
Lower Bounds ◽  
Formal Languages ◽  
The State ◽  
Upper And Lower Bounds ◽  
State Complexity ◽  
Finite Set

In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state complexity of root(L) over alphabets of all sizes. As well, we present an application of these results to the problem of 2DFA-DFA conversion.

Lower Bounds on the State Complexity of Linear Tail-Biting Trellises

2004 ◽  
Vol 50 (3) ◽  
pp. 566-571 ◽  
Author(s):  
Y. Shany ◽  
I. Reuven ◽  
Y. Be'ery
Keyword(s):  
Lower Bounds ◽  
The State ◽  
State Complexity ◽  
Tail Biting

On the state complexity of intersection of regular languages

1991 ◽  
Vol 22 (3) ◽  
pp. 52-54 ◽  
Author(s):  
Sheng Yu ◽  
Qingyu Zhuang
Keyword(s):  
The State ◽  
Regular Languages ◽  
State Complexity

scholarly journals Lower bounds for the state complexity of probabilistic languages and the language of prime numbers

2020 ◽  
Vol 30 (1) ◽  
pp. 175-192
Author(s):  
NathanaËl Fijalkow
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Prime Numbers ◽  
Regular Languages ◽  
Automata Theory ◽  
Seminal Paper ◽  
Probabilistic Automata ◽  
State Complexity ◽  
Probabilistic Languages ◽  
Alternating Automata

Abstract This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal paper of Rabin from 1963 introducing probabilistic automata, we study the (deterministic) state complexity of probabilistic languages and prove that probabilistic languages can have arbitrarily high deterministic state complexity. We then look at alternating automata as introduced by Chandra, Kozen and Stockmeyer: such machines run independent computations on the word and gather their answers through boolean combinations. We devise a lower bound technique relying on boundedly generated lattices of languages, and give two applications of this technique. The first is a hierarchy theorem, stating that there are languages of arbitrarily high polynomial alternating state complexity, and the second is a linear lower bound on the alternating state complexity of the prime numbers written in binary. This second result strengthens a result of Hartmanis and Shank from 1968, which implies an exponentially worse lower bound for the same model.

scholarly journals State Complexity of Neighbourhoods and Approximate Pattern Matching

2018 ◽  
Vol 29 (02) ◽  
pp. 315-329 ◽  
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Pattern Matching ◽  
Finite Automaton ◽  
The State ◽  
Worst Case ◽  
State Complexity ◽  
Approximate Pattern Matching ◽  
The Given ◽  
Nondeterministic Finite Automaton ◽  
Distance Formula

The neighbourhood of a language [Formula: see text] with respect to an additive distance consists of all strings that have distance at most the given radius from some string of [Formula: see text]. We show that the worst case deterministic state complexity of a radius [Formula: see text] neighbourhood of a language recognized by an [Formula: see text] state nondeterministic finite automaton [Formula: see text] is [Formula: see text]. In the case where [Formula: see text] is deterministic we get the same lower bound for the state complexity of the neighbourhood if we use an additive quasi-distance. The lower bound constructions use an alphabet of size linear in [Formula: see text]. We show that the worst case state complexity of the set of strings that contain a substring within distance [Formula: see text] from a string recognized by [Formula: see text] is [Formula: see text].

scholarly journals Most Complex Non-Returning Regular Languages

2019 ◽  
Vol 30 (06n07) ◽  
pp. 921-957
Author(s):  
Janusz A. Brzozowski ◽  
Sylvie Davies
Keyword(s):  
Star Product ◽  
Upper Bounds ◽  
The State ◽  
Boolean Operations ◽  
Deterministic Finite Automaton ◽  
Initial State ◽  
Complexity Measures ◽  
State Complexity ◽  
Complex Sequence ◽  
Binary Operations

A regular language [Formula: see text] is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jirásková derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived tight upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each [Formula: see text], there exists a ternary witness of state complexity [Formula: see text] that meets the bound for reversal, and restrictions of this witness to binary alphabets meet the bounds for star, product, and boolean operations. Hence all of these operations can be handled simultaneously with a single witness, using only three different transformations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has [Formula: see text] elements and requires at least [Formula: see text] generators. We find the maximal state complexities of atoms of non-returning languages. We show that there exists a most complex sequence of non-returning languages that meet the bounds for all of these complexity measures. Furthermore, we prove there is a most complex sequence that meets all the bounds using alphabets of minimal size.

STATE COMPLEXITY OF ADDITIVE WEIGHTED FINITE AUTOMATA

2007 ◽  
Vol 18 (06) ◽  
pp. 1407-1416 ◽  
Author(s):  
KAI SALOMAA ◽  
PAUL SCHOFIELD
Keyword(s):  
Upper Bound ◽  
Finite Automaton ◽  
Regular Language ◽  
Finite Automata ◽  
The State ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Weighted Finite Automata

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for the state complexity of the conversion.

scholarly journals State Complexity of Suffix Distance

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1197-1216
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Finite Automaton ◽  
Regular Language ◽  
Upper Bounds ◽  
The State ◽  
Deterministic Finite Automaton ◽  
Tight Bound ◽  
State Complexity

The neighbourhood of a regular language with respect to the prefix, suffix and subword distance is always regular and a tight bound for the state complexity of prefix distance neighbourhoods is known. We give upper bounds for the state complexity of the neighbourhood of radius [Formula: see text] of an [Formula: see text]-state deterministic finite automaton language with respect to the suffix distance and the subword distance, respectively. For restricted values of [Formula: see text] and [Formula: see text] we give a matching lower bound for the state complexity of suffix distance neighbourhoods.

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