scholarly journals Good-for-games $\omega$-Pushdown Automata

2022 ◽  
Vol Volume 18, Issue 1 ◽  
Author(s):  
Karoliina Lehtinen ◽  
Martin Zimmermann
Keyword(s):  
Infinite Games ◽  
Closure Properties ◽  
New Class ◽  
Deterministic Automata ◽  
Good For ◽  
Pushdown Automata

We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results are that $\omega$-GFG-PDA are more expressive than deterministic $\omega$- pushdown automata and that solving infinite games with winning conditions specified by $\omega$-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for $\omega$-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG- PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages. Finally, we compare $\omega$-GFG-PDA to $\omega$-visibly PDA, study the resources necessary to resolve the nondeterminism in $\omega$-GFG-PDA, and prove that the parity index hierarchy for $\omega$-GFG-PDA is infinite.

Self-Verifying Pushdown and Queue Automata

2021 ◽  
Vol 180 (1-2) ◽  
pp. 1-28
Author(s):  
Henning Fernau ◽  
Martin Kutrib ◽  
Matthias Wendlandt
Keyword(s):  
Recursive Function ◽  
Input Word ◽  
Closure Properties ◽  
Descriptional Complexity ◽  
Trade Offs ◽  
Deterministic Automata ◽  
Context Free ◽  
Pushdown Automata ◽  
Computation Path

We study the computational and descriptional complexity of self-verifying pushdown automata (SVPDA) and self-verifying realtime queue automata (SVRQA). A self-verifying automaton is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that SVPDA and SVRQA are automata characterizations of so-called complementation kernels, that is, context-free or realtime nondeterministic queue automaton languages whose complement is also context free or accepted by a realtime nondeterministic queue automaton. So, the families of languages accepted by SVPDA and SVRQA are strictly between the families of deterministic and nondeterministic languages. Closure properties and various decidability problems are considered. For example, it is shown that it is not semidecidable whether a given SVPDA or SVRQA can be made self-verifying. Moreover, we study descriptional complexity aspects of these machines. It turns out that the size trade-offs between nondeterministic and self-verifying as well as between self-verifying and deterministic automata are non-recursive. That is, one can choose an arbitrarily large recursive function f, but the gain in economy of description eventually exceeds f when changing from the former system to the latter.

scholarly journals Further closure properties of input-driven pushdown automata

2019 ◽  
Vol 798 ◽  
pp. 65-77
Author(s):  
Alexander Okhotin ◽  
Kai Salomaa
Keyword(s):  
Closure Properties ◽  
Pushdown Automata

The NBUC and NWUC classes of life distributions

1991 ◽  
Vol 28 (02) ◽  
pp. 473-479 ◽  
Author(s):  
Jinhua Cao ◽  
Yuedong Wang
Keyword(s):  
Shock Model ◽  
Stieltjes Transform ◽  
Closure Properties ◽  
Convex Ordering ◽  
New Class ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

A new class of life distributions, namely new better than used in convex ordering (NBUC), and its dual, new worse than used in convex ordering (NWUC), are introduced. Their relations to other classes of life distributions, closure properties under three reliability operations, and heritage properties under shock model and Laplace-Stieltjes transform are discussed.

scholarly journals On a New Class ofp-Valent Meromorphic Functions Defined in Conic Domains

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Mohammed Ali Alamri ◽  
Maslina Darus
Keyword(s):  
Hypergeometric Function ◽  
Meromorphic Functions ◽  
Starlike Functions ◽  
Closure Properties ◽  
New Class ◽  
Conic Domain ◽  
Class Of Functions

We define a new class of multivalent meromorphic functions using the generalised hypergeometric function. We derived this class related to conic domain. It is also shown that this new class of functions, under certain conditions, becomes a class of starlike functions. Some results on inclusion and closure properties are also derived.

scholarly journals A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1812
Author(s):  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Shahid Khan ◽  
Qazi Zahoor Ahmad ◽  
Bilal Khan
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Function Class ◽  
Distortion Theorem ◽  
Additional Parameter ◽  
Sufficient Condition ◽  
Closure Properties ◽  
Derivative Operator ◽  
New Class ◽  
Symmetric Points

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called (p,q)-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary.

The NBUC and NWUC classes of life distributions

1991 ◽  
Vol 28 (2) ◽  
pp. 473-479 ◽  
Author(s):  
Jinhua Cao ◽  
Yuedong Wang
Keyword(s):  
Shock Model ◽  
Stieltjes Transform ◽  
Closure Properties ◽  
Convex Ordering ◽  
New Class ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

A new class of life distributions, namely new better than used in convex ordering (NBUC), and its dual, new worse than used in convex ordering (NWUC), are introduced. Their relations to other classes of life distributions, closure properties under three reliability operations, and heritage properties under shock model and Laplace-Stieltjes transform are discussed.

scholarly journals Digging input-driven pushdown automata

2021 ◽  
Vol 55 ◽  
pp. 6
Author(s):  
Martin Kutrib ◽  
Andreas Malcher
Keyword(s):  
Input Symbol ◽  
Closure Properties ◽  
Descriptional Complexity ◽  
Finite State Transducers ◽  
Finite State ◽  
The Impact ◽  
Pushdown Automata

Input-driven pushdown automata (IDPDA) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Nowadays such devices are usually defined such that popping from the empty pushdown does not block the computation but continues it with empty pushdown. Here, we consider IDPDAs that have a more balanced behavior concerning pushing and popping. Digging input-driven pushdown automata (DIDPDA) are basically IDPDAs that, when forced to pop from the empty pushdown, dig a hole of the shape of the popped symbol in the bottom of the pushdown. Popping further symbols from a pushdown having a hole at the bottom deepens the current hole furthermore. The hole can only be filled up by pushing symbols previously popped. We study the impact of the new behavior of DIDPDAs on their power and compare their capacities with the capacities of ordinary IDPDAs and tinput-driven pushdown automata which are basically IDPDAs whose input may be preprocessed by length-preserving finite state transducers. It turns out that the capabilities are incomparable. We address the determinization of DIDPDAs and their descriptional complexity, closure properties, and decidability questions.

Searching for Absolute ᘓℛ–Epic Spaces

2007 ◽  
Vol 59 (3) ◽  
pp. 465-487 ◽  
Author(s):  
Michael Barr ◽  
John F. Kennison ◽  
R. Raphael
Keyword(s):  
Topological Space ◽  
Commutative Rings ◽  
Closure Properties ◽  
Countable Intersection ◽  
Compact Spaces ◽  
New Class ◽  
Finite Products ◽  
Perfect Map

AbstractIn previous papers, Barr and Raphael investigated the situation of a topological space Y and a subspace X such that the induced map C(Y ) → C(X) is an epimorphism in the category ᘓℛ of commutative rings (with units). We call such an embedding a ᘓℛ-epic embedding and we say that X is absolute ᘓℛ-epic if every embedding of X is ᘓℛ-epic. We continue this investigation. Our most notable result shows that a Lindelöf space X is absolute ᘓℛ-epic if a countable intersection of βX-neighbourhoods of X is a βX-neighbourhood of X. This condition is stable under countable sums, the formation of closed subspaces, cozero-subspaces, and being the domain or codomain of a perfect map. A strengthening of the Lindelöf property leads to a new class with the same closure properties that is also closed under finite products. Moreover, all σ-compact spaces and all Lindelöf P-spaces satisfy this stronger condition. We get some results in the non-Lindelöf case that are sufficient to show that the Dieudonné plank and some closely related spaces are absolute ᘓℛ-epic.

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