Periodic properties of pushdown automata

2019 ◽  
Vol 29 (6) ◽  
pp. 351-356
Author(s):  
Ilya E. Ivanov
Keyword(s):  
Lower Bound ◽  
Linear Function ◽  
Finite Automata ◽  
Quadratic Function ◽  
Periodic Sequences ◽  
Output Sequence ◽  
Pushdown Automata

Abstract Finite automata transform periodic sequences into periodic ones. The period of the output sequence is bounded from above by a linear function of input period. It is known that pushdown automata also preserve the set of periodic sequences. We prove that the output period for one-counter pushdown automata is bounded from above by a quadratic function of input period. We also give an example of an automaton with a quadratic lower bound on output period.

scholarly journals Lower Bounds for the Average Genus of a CF-graph

10.37236/422 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Yichao Chen
Keyword(s):  
Lower Bound ◽  
Linear Function ◽  
Lower Bounds ◽  
Betti Number ◽  
Maximum Genus ◽  
Simple Graphs ◽  
Structure Theorems ◽  
Average Genus

CF-graphs form a class of multigraphs that contains all simple graphs. We prove a lower bound for the average genus of a CF-graph which is a linear function of its Betti number. A lower bound for average genus in terms of the maximum genus and some structure theorems for graphs with a given average genus are also provided.

scholarly journals Subtree matching by pushdown automata

2010 ◽  
Vol 7 (2) ◽  
pp. 331-357 ◽  
Author(s):  
Tomás Flouri ◽  
Jan Janousek ◽  
Bořivoj Melichar
Keyword(s):  
Programming Languages ◽  
Theorem Proving ◽  
Systematic Approach ◽  
Finite Automata ◽  
Term Rewriting ◽  
Mechanical Theorem Proving ◽  
Pushdown Automaton ◽  
String Pattern ◽  
Pushdown Automata ◽  
Mechanical Theorem

Subtree matching is an important problem in Computer Science on which a number of tasks, such as mechanical theorem proving, term-rewriting, symbolic computation and nonprocedural programming languages are based on. A systematic approach to the construction of subtree pattern matchers by deterministic pushdown automata, which read subject trees in prefix and postfix notation, is presented. The method is analogous to the construction of string pattern matchers: for a given pattern, a nondeterministic pushdown automaton is created and is then determinised. In addition, it is shown that the size of the resulting deterministic pushdown automata directly corresponds to the size of the existing string pattern matchers based on finite automata.

ON THE -ERROR LINEAR COMPLEXITY OF SEQUENCES FROM FUNCTION FIELDS

2020 ◽  
Vol 102 (2) ◽  
pp. 342-352
Author(s):  
YUHUI ZHOU ◽  
YUHUI HAN ◽  
YANG DING
Keyword(s):  
Lower Bound ◽  
Linear Complexity ◽  
Function Fields ◽  
Stream Ciphers ◽  
Security Measures ◽  
Periodic Sequences ◽  
Error Linear Complexity

The linear complexity and the error linear complexity are two important security measures for stream ciphers. We construct periodic sequences from function fields and show that the error linear complexity of these periodic sequences is large. We also give a lower bound for the error linear complexity of a class of nonperiodic sequences.

scholarly journals SUBLINEARLY SPACE BOUNDED ITERATIVE ARRAYS

2010 ◽  
Vol 21 (05) ◽  
pp. 843-858 ◽  
Author(s):  
ANDREAS MALCHER ◽  
CARLO MEREGHETTI ◽  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Computational Model ◽  
Regular Language ◽  
Finite Automata ◽  
Complexity Classes ◽  
Language Recognition ◽  
Deterministic Finite Automata ◽  
One Dimensional ◽  
Sequential Processing ◽  
Trade Offs

Iterative arrays (IAs) are a parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this paper, realtime-IAs with sublinear space bounds are used to recognize formal languages. The existence of an infinite proper hierarchy of space complexity classes between logarithmic and linear space bounds is proved. Some decidability questions on logarithmically space bounded realtime-IAs are investigated, and an optimal logarithmic space lower bound for non-regular language recognition on realtime-IAs is shown. Finally, some non-recursive trade-offs between space bounded realtime-IAs are emphasized.

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn

2006 ◽  
Vol 49 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Allison M. Pacelli
Keyword(s):  
Lower Bound ◽  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Prime Degree ◽  
Cyclic Function ◽  
Quadratic Function Fields

AbstractIn this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.

Emptiness of Ordered Multi-Pushdown Automata is 2ETIME-Complete

2017 ◽  
Vol 28 (08) ◽  
pp. 945-975 ◽  
Author(s):  
Mohamed Faouzi Atig ◽  
Benedikt Bollig ◽  
Peter Habermehl
Keyword(s):  
Lower Bound ◽  
Turing Machine ◽  
Linear Ordering ◽  
Emptiness Problem ◽  
Pushdown Automata ◽  
Exponential Space

We consider ordered multi-pushdown automata, a multi-stack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first non-empty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multi-pushdown automata is 2ETIME-complete. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare ordered multi-pushdown automata with the model of bounded-phase (visibly) multi-stack pushdown automata, which do not impose an ordering on stacks, but restrict the number of alternations of pop operations on different stacks.

SIMULATIONS OF UNARY ONE-WAY MULTI-HEAD FINITE AUTOMATA

2014 ◽  
Vol 25 (07) ◽  
pp. 877-896 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER ◽  
MATTHIAS WENDLANDT
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Unary Languages ◽  
Order Of Magnitude ◽  
Simulation Results ◽  
Special Case ◽  
Nondeterministic Finite Automaton

We investigate the descriptional complexity of deterministic one-way multi-head finite automata accepting unary languages. It is known that in this case the languages accepted are regular. Thus, we study the increase of the number of states when an n-state k-head finite automaton is simulated by a classical (one-head) deterministic or nondeterministic finite automaton. In the former case upper and lower bounds that are tight in the order of magnitude are shown. For the latter case we obtain an upper bound of O(n2k) and a lower bound of Ω(nk) states. We investigate also the costs for the conversion of one-head nondeterministic finite automata to deterministic k-head finite automata, that is, we trade nondeterminism for heads. In addition, we study how the conversion costs vary in the special case of finite and, in particular, of singleton unary lanuages. Finally, as an application of the simulation results, we show that decidability problems for unary deterministic k-head finite automata such as emptiness or equivalence are LOGSPACE-complete.

State Complexity of Insertion

2016 ◽  
Vol 27 (07) ◽  
pp. 863-878 ◽  
Author(s):  
Yo-Sub Han ◽  
Sang-Ki Ko ◽  
Timothy Ng ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Regular Language ◽  
Finite Automata ◽  
The State ◽  
Tight Bound ◽  
State Complexity ◽  
Nondeterministic State

It is well known that the resulting language obtained by inserting a regular language to a regular language is regular. We study the nondeterministic and deterministic state complexity of the insertion operation. Given two incomplete DFAs of sizes m and n, we give an upper bound (m+2)·2mn−m−1·3m and find a lower bound for an asymp-totically tight bound. We also present the tight nondeterministic state complexity by a fooling set technique. The deterministic state complexity of insertion is 2Θ(mn) and the nondeterministic state complexity of insertion is precisely mn+2m, where m and n are the size of input finite automata. We also consider the state complexity of insertion in the case where the inserted language is bifix-free or non-returning.

scholarly journals Overstocking in the trans-Himalayan rangelands of India

2001 ◽  
Vol 28 (3) ◽  
pp. 279-283 ◽  
Author(s):  
Charudutt Mishra ◽  
Herbert H.T. Prins ◽  
Sipke E. van Wieren
Keyword(s):  
Linear Function ◽  
Adult Female ◽  
Empirical Data ◽  
Conservation Management ◽  
Quadratic Function ◽  
Animal Production ◽  
Biomass Density ◽  
Economic Changes ◽  
Production Models ◽  
The Commons

High livestock densities in rangelands can result in reduced animal production due either to overgrazing or reduced per caput food availability, yet evidence for reduced animal production due to overstocking is scarce. Here simple animal production models establish the occurrence of overstocking in a traditional agropastoral system in the Spiti Valley of the Indian Trans-Himalaya. Empirical data show that fecundity of adult female livestock is related to total livestock biomass density (S) as a negative linear function of S. Total herd production is modelled as a quadratic function of S, thereby calculating an optimum livestock biomass density (Sop), at which total herd production is maximized. A sample of 40 villages showed that over 83% of Spiti's rangelands may be overstocked with values of S > Sop. Overstocking seems to be a classic case of the tragedy of the commons, as livestock is individually owned while the land is communally grazed. Recent socio-economic changes have probably contributed to high levels of overstocking. Even areas within wildlife reserves are overstocked. Conservation management needs to focus on creation of grazing free areas and management of livestock densities.

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