scholarly journals Collapsible Pushdown Parity Games

2021 ◽  
Vol 22 (3) ◽  
pp. 1-51
Author(s):  
Christopher H. Broadbent ◽  
Arnaud Carayol ◽  
Matthew Hague ◽  
Andrzej S. Murawski ◽  
C.-H. Luke Ong ◽  
...  
Keyword(s):  
Large Class ◽  
Winning Strategy ◽  
Higher Order ◽  
Infinite Graphs ◽  
Main Motivation ◽  
Infinite Trees ◽  
Depth Study ◽  
Parity Games ◽  
Pushdown Automata ◽  
Effective Representation

This article studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely, those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite trees. Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy. Thus, the results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes.

scholarly journals Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

2021 ◽  
Vol 22 (2) ◽  
pp. 1-37
Author(s):  
Christopher H. Broadbent ◽  
Arnaud Carayol ◽  
C.-H. Luke Ong ◽  
Olivier Serre
Keyword(s):  
Model Checking ◽  
Free Variable ◽  
Higher Order ◽  
Second Order ◽  
Effective Solution ◽  
Parity Games ◽  
Transition Graphs ◽  
Second Order Logic ◽  
Pushdown Automata ◽  
Monadic Second Order Logic

This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal -calculus, three main problems: model-checking, logical reflection (a.k.a. global model-checking, that asks for a finite description of the set of elements for which a formula holds), and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems, we provide an effective solution. This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.

Type Inference: Some Results, Some Problems1

1993 ◽  
Vol 19 (1-2) ◽  
pp. 87-125
Author(s):  
Paola Giannini ◽  
Furio Honsell ◽  
Simona Ronchi Della Rocca
Keyword(s):  
Large Class ◽  
Higher Order ◽  
Type Inference ◽  
Principal Type ◽  
Open Problems ◽  
Inference Problem ◽  
Type Assignment ◽  
Unification Problem

In this paper we investigate the type inference problem for a large class of type assignment systems for the λ-calculus. This is the problem of determining if a term has a type in a given system. We discuss, in particular, a collection of type assignment systems which correspond to the typed systems of Barendregt’s “cube”. Type dependencies being shown redundant, we focus on the strongest of all, Fω, the type assignment version of the system Fω of Girard. In order to manipulate uniformly type inferences we give a syntax directed presentation of Fω and introduce the notions of scheme and of principal type scheme. Making essential use of them, we succeed in reducing the type inference problem for Fω to a restriction of the higher order semi-unification problem and in showing that the conditional type inference problem for Fω is undecidable. Throughout the paper we call attention to open problems and formulate some conjectures.

Researching transformative change over time

2021 ◽  
pp. 145-166
Author(s):  
Priscilla Alderson
Keyword(s):  
Lower Order ◽  
Higher Order ◽  
Fourth Dimension ◽  
Transformative Change ◽  
Personal Change ◽  
Change Over Time ◽  
Depth Study ◽  
Immanent Critique ◽  
First Moment ◽  
Over Time

Chapter 6 on the four stages of dialectical transformative change involves concepts of: absence as well as presence; difference versus actual transformative change; emergence of higher order things from lower order ones; immanent critique. With the four stages, the acronym MELD stands for first Moment, second Edge, third Level and fourth Dimension. The stages are considered in their benign/effective, malign/ineffective and mini versions. It is vital to start research with 1M’s intense in-depth study before intervening at 2E, then at 3L looking at the larger scene, and at 4D working on personal change. There is an overview of research from past to future, local to global. The detailed example applies MELD to research on improving care for children with allergies.

TWO LOCAL STRATEGY ITERATION SCHEMES FOR PARITY GAME SOLVING

2012 ◽  
Vol 23 (03) ◽  
pp. 669-685 ◽  
Author(s):  
OLIVER FRIEDMANN ◽  
MARTIN LANGE
Keyword(s):  
Model Checking ◽  
Winning Strategy ◽  
Fractional Part ◽  
Program Synthesis ◽  
Global Strategy ◽  
Local Algorithm ◽  
The Core ◽  
Local Strategy ◽  
Parity Games ◽  
Satisfiability Checking

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy iteration algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present two local strategy iteration algorithms which explore the game graph on-the-fly whilst performing the improvement steps. We also compare them empirically with existing global strategy iteration algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy iteration can outperform these others significantly.

scholarly journals The Detailed Organization of the Human Cerebellum Estimated by Intrinsic Functional Connectivity Within the Individual

2020 ◽  
Author(s):  
Aihuiping Xue ◽  
Ru Kong ◽  
Qing Yang ◽  
Mark C. Eldaief ◽  
Peter Angeli ◽  
...  
Keyword(s):  
Functional Connectivity ◽  
Anterior Lobe ◽  
Higher Order ◽  
The Body ◽  
Central Field ◽  
Posterior Lobe ◽  
Multiple Networks ◽  
Depth Study ◽  
Crus I ◽  
The Individual

Distinct regions of the cerebellum connect to separate regions of the cerebral cortex forming a complex topography. While key properties of cerebellar organization have been revealed in group-averaged data, in-depth study of individuals provides an opportunity to discover functional-anatomical features that emerge at a higher spatial resolution. Here functional connectivity MRI was used to examine the cerebellum of two intensively-sampled individuals (each scanned across 31 MRI sessions). Connectivity to somatomotor cortex showed the expected crossed laterality and inversion of the body maps between the anterior and posterior lobes. A surprising discovery was connectivity to the primary visual cortex along the vermis with evidence for representation of the central field. Within the hemispheres, each individual displayed a hierarchical progression from the inverted anterior lobe somatomotor map through to higher-order association zones. The hierarchy ended near Crus I/II and then progressed in reverse order through to the upright somatomotor map in the posterior lobe. Evidence for a third set of networks was found in the most posterior extent of the cerebellum. Detailed analysis of the higher-order association networks around the Crus I/II apex revealed robust representations of two distinct networks linked to the default network, multiple networks linked to cognitive control, as well as a separate representation of a language network. While idiosyncratic spatial details emerged between subjects, each of these networks could be detected in both individuals, and small seed regions placed within the cerebellum recapitulated the full extent of the spatially-specific cerebral networks. The observation of multiple networks in juxtaposed regions at the Crus I/II apex confirms the importance of this zone to higher-order cognitive function and reveals new organizational details.

scholarly journals Partial Face Recognition

2019 ◽  
Vol 8 (2S8) ◽  
pp. 1581-1584
Keyword(s):  
Face Recognition ◽  
Higher Order ◽  
Point Matching ◽  
Topological Information ◽  
Key Points ◽  
Depth Study ◽  
Facial Images ◽  
Order Paper ◽  
Selection Of ◽  
Made In

Most current Face Identification methods get features and nodes points from still and clear facial images. But, individuals in real world may be obstructed from objects or other people who do not provide the entire image of the person to describe. Keyword-following pats key recognition methods such as: Multiple Key Points with Gbor Triangle (MKD-GTP) and Group Point Matching (RPSM) correspond to the local key points for part of face recognition.Also, on the same note they measure similarity of nodes without higher order mathematical and graphicalinformation that are prone to noise. To solve this, the TPGM method evaluates a static change that encodes the geometry of the other line of the graph, so that a extra precise and stable match with the topology can be calculated.In case to apply higher topological information having higher order, paper offer a topological method to preserve the TPSM algorithm ofconstructionofa higher order shape for each surface and evaluate the change. The paper also suggests that the selection of Viola Jones face recognition points. Deep training can be used to create and combine graphs. This article offers an in-depth study of the progress made in scientific articles and explains the accuracy of the results

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