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Representation of graph notation
A Program Dependence Graph (PDG) is a directed graph of a program's control and data dependencies. Nodes represent program statements and edges represent
Program_dependence_graph
Representation of a computer program
(CFG) and program dependence graphs (PDG) at statement and predicate nodes. The resulting graph is a property graph, which is the underlying graph model of
Code_property_graph
Graphical representation of a computer program or algorithm
diagram Control-flow analysis Data-flow analysis Interval (graph theory) Program dependence graph Cyclomatic complexity Static single assignment Compiler
Control-flow_graph
Restructuring existing computer code without changing its external behavior
Warren, Joe D. (July 1987). "The program dependence graph and its use in optimization". ACM Transactions on Programming Languages and Systems. 9 (3). ACM:
Code_refactoring
global correctness. Control-flow graph Program slicing Program dependence graph Structured programming Structured program theorem Ferrante, Ottenstein &
Single-entry_single-exit
Process to determine relationships among statements
iteration space traversal graph and the loop carried dependence graph is: Iteration Space Traversal Graph: Loop Carried Dependence Graph: Work by Moyen, Rubiano
Loop_dependence_analysis
American computer scientist (1932–2020)
execution of FORTRAN programs. Her PTRAN team developed new parallelism detection schemes and created the concept of the program dependence graph, the primary
Frances_Allen
Compiler optimization to remove code which does not affect the program results
(1991). Efficiently Computing Static Single Assignment Form and the Program Dependence Graph. ACM TOPLAS 13(4). Cooper, Keith D.; Torczon, Linda (2003) [2002-01-01]
Dead-code_elimination
execution of FORTRAN programs. Her PTRAN team developed new parallelism detection schemes and created the concept of the program dependence graph, the primary
History of compiler construction
History_of_compiler_construction
Topics referred to by the same term
Particle Data Group, international group of particle physicists Program dependence graph, in computer science, a diagram to clarify dependencies Patrouille
PDG
dependencies. Dependence analysis determines whether it is safe to reorder or parallelize statements. Control dependency is a situation in which a program instruction
Dependence_analysis
Set of software engineering methods
and David Binkley, Interprocedural slicing using dependence graphs, ACM Transactions on Programming Languages and Systems, Volume 12, Issue 1, pages 26-60
Program_slicing
Loop-carried dependence graph graphically shows the loop-carried dependencies between iterations. Each iteration is listed as a node on the graph, and directed
Loop-level_parallelism
Directed graph representing dependencies
mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other
Dependency_graph
Computer science field
or a special-purpose language. Such a program corresponds to a finite-state machine (FSM), i.e., a directed graph consisting of nodes (or vertices) and
Model_checking
Analysis of computer programs without executing them
computer science, static program analysis (also known as static analysis or static simulation) is the analysis of computer programs performed without executing
Static_program_analysis
Medical condition
diarrhea, trouble sleeping, agitation, and a low mood. Addiction and dependence are important components of opioid use disorder. Risk factors include
Opioid_use_disorder
When every path in a control-flow graph must go through one node to reach another
In computer science, a node d of a control-flow graph dominates a node n if every path from the entry node to n must go through d. Notationally, this
Dominator_(graph_theory)
Graph data structure
In computer science, an e-graph is a data structure that stores an equivalence relation over terms of some language. Let Σ {\displaystyle \Sigma } be
E-graph
Problem of finding the longest simple path for a given graph
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A
Longest_path_problem
Process of analyzing computer program behavior
execution of a program. The collected information is represented by a control-flow graph (CFG) where the nodes are instructions of the program and the edges
Program_analysis
Dependence of the state of a system on its history
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given
Hysteresis
{\displaystyle S_{1}} Control dependences are essentially the dominance frontier in the reverse graph of the control-flow graph (CFG). Thus, one way of constructing
Control_dependency
Validates computer program operations
analysis, sometimes called protocol analysis, is a form of program analysis employed in programming languages. It is most commonly applied to object-oriented
Typestate_analysis
SIGPLAN 2012 PL Achievement Award Jeanne Ferrante, developed the Program dependence graph, ACM SIGPLAN 2006 PL Achievement Award Robby Findler, thesis on
List of programming language researchers
List_of_programming_language_researchers
Computer program for the Boolean satisfiability problem
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem (SAT). On input a formula
SAT_solver
Mathematical optimization problem restricted to integers
integer programming that will serve as the proof of NP-hardness. Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected graph. Define a linear program as
Integer_programming
Concept in computer science
BI Pointer Logic: the Schorr−Waite Graph Marking Algorithm". Proceedings of the 1st Workshop on Semantics' Program Analysis' and Computing Environments
Separation_logic
Flow graph invented by Claude Shannon
Mason to illustrate basic concepts: In the simple flow graphs of the figure, a functional dependence of a node is indicated by an incoming arrow, the node
Signal-flow_graph
S2CID 5753565. Johnson, Richard Craig (1995). Efficient Program Analysis using Dependence Flow Graphs (Ph.D.). Cornell University. Gutwenger, Carsten; Mutzel
Program_structure_tree
Mapping of a graph into a tree
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain
Tree_decomposition
Representation of a graph as a path graph "thickened" by some amount
without dependence on k. Many problems in graph algorithms may be solved efficiently on graphs of bounded pathwidth, by using dynamic programming on a path-decomposition
Pathwidth
Overview of and topical guide to machine learning
Averaged one-dependence estimators (AODE) Artificial neural network Case-based reasoning Gaussian process regression Gene expression programming Group method
Outline_of_machine_learning
Subset of a graph's vertices, including at least one endpoint of every edge
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In
Vertex_cover
Algorithm in graph theory
algorithms for the same problem, but with a higher dependence on the numbers of edges and vertices in the graph, have been known for longer. The network simplex
Network_simplex_algorithm
Abstraction of linear independence of vectors
theory borrows extensively from the terms used in both linear algebra and graph theory, largely because it is the abstraction of various notions of central
Matroid
On linear-time algorithms for graph logic
study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided
Courcelle's_theorem
C++ library providing parallelism support
extended to allow efficient parallelism. pRange - a parallel task dependence graph recursively defined as a tree of subranges. pAlgorithms - parallel
Stapl
Measure of graph complexity
2k. The graphs of treewidth w have clique-width at most 3 · 2w − 1. The exponential dependence in this bound is necessary: there exist graphs whose clique-width
Clique-width
Number denoting a graph's closeness to a tree
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest
Treewidth
k {\displaystyle k} . Alternatively, with polynomial dependence on the graph size, the dependence on k {\displaystyle k} can be made as small as 2.3146
Odd_cycle_transversal
Property of an intermediate representation in a compiler
static single assignment form and the control dependence graph" (PDF). ACM Transactions on Programming Languages and Systems. 13 (4): 451–490. CiteSeerX 10
Static_single-assignment_form
Of a function, an additional effect besides returning a value
analysis of programming languages. The degree to which side effects are used depends on the programming paradigm. For example, imperative programming is commonly
Side effect (computer science)
Side_effect_(computer_science)
Concepts in theoretical computer science
Properties of an execution of a computer program—particularly for concurrent and distributed systems—have long been formulated by giving safety properties
Safety and liveness properties
Safety_and_liveness_properties
Computer algebra system
faster speeds for most index contractions with an approach based on the graph isomorphism problem rather than canonicalisation. Free and open-source software
Cadabra_(computer_program)
Case in parallel computing
4, safe to ignore a[i] = a[i-1]; // 1 < 4, stays on dependency graph } Using the graph, the optimizer can then cluster the strongly connected components
Automatic_vectorization
Rules to verify computer program correctness
logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician
Hoare_logic
reduction, transitive closures on maps (which may encode infinite graphs), dependence analysis and bounds on piecewise step-polynomials. All computations
Integer_set_library
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
Abstraction of ordered linear algebra
ordinary (i.e., non-oriented) matroid abstracts the dependence properties that are common both to graphs, which are not necessarily directed, and to arrangements
Oriented_matroid
Largest independent set of paired elements
The problem was formulated by Lawler (1976) as a common generalization of graph matching and matroid intersection. It is also known as polymatroid matching
Matroid_parity_problem
Approach to static program analysis
computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which
Abstract_interpretation
Numerical invariant of graphs
In graph theory, the tree-depth of a connected undirected graph G {\displaystyle G} is a numerical invariant of G {\displaystyle G} , the minimum height
Tree-depth
Process of generalization
they are not abstract in the sense of the objects in graph 1 below. We might look at other graphs, in a progression from cat to mammal to animal, and see
Abstraction
Hierarchical clustering of graph edges
In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree
Branch-decomposition
2026 documentary film by Adrian Choa
According to Theroux, his own search interest was "down near death" in the graph whereas Tate's was "quite high all the way along". However, at the very
Louis Theroux: Inside the Manosphere
Louis_Theroux:_Inside_the_Manosphere
Fewest cliques covering a graph's edges
double-exponential dependence is necessary regardless of whether kernelization is used. On graphs of bounded treewidth, dynamic programming on a tree decomposition
Intersection number (graph theory)
Intersection_number_(graph_theory)
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Directional variation in strength of radio waves
(or antenna pattern or far-field pattern) is the directional (angular) dependence of the field strength (sometimes also the phase) of the radio waves from
Radiation_pattern
Probabilistic graphical representation of causal relationships
of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks
Bayesian_network
Compiler optimization technique
dependency graph is a directed acyclic graph. Then, any topological sort of this graph is a valid instruction schedule. The edges of the graph are usually
Instruction_scheduling
Concerned with the notion of stability in model theory
any nowhere dense graph class. These include graph classes with bounded expansion, which in turn include planar graphs and any graph class of bounded degree
Stable_theory
of the program being analyzed and the algorithms used in the test. Finally, the results of dependence analysis will be reported in a dependence abstraction
Frameworks supporting the polyhedral model
Frameworks_supporting_the_polyhedral_model
Fundamental problem in computer science
control-flow paths in a program grows exponentially ("explodes") with an increase in program size and can even be infinite in the case of programs with unbounded
Path_explosion
US public health issue
Centers for Disease Control and Prevention. Hover cursor over the end of the graph in Figure 1A to get the latest number. Scroll down the page and click on
United States drug overdose death rates and totals over time
United_States_drug_overdose_death_rates_and_totals_over_time
sense because there's no inclusion-test that could be applied to a single program trace; non-interference is an assertion about how neighboring traces are
Hyperproperty
Compiler that optimizes generated code
value numbering GVN eliminates redundancy by constructing a value graph of the program, and then determining which values are computed by equivalent expressions
Optimizing_compiler
twin-width of an undirected graph is a natural number associated with the graph, used to study the parameterized complexity of graph algorithms. Intuitively
Twin-width
Use of an excessive amount of a drug
Control and Prevention. Click on "Rising Rates" tab for a graph. See data table below the graph. NCHS Data Visualization Gallery—Drug Poisoning Mortality
Drug_overdose
Circular statistical graph of proportionality
Cleveland, William S. (1985). The Elements of Graphing Data. Pacific Grove, CA: Wadsworth & Advanced Book Program. ISBN 0-534-03730-5. Friendly, Michael. "The
Pie_chart
Type of chart
measures. Radar charts are also known as web charts, spider charts, spider graphs, spider web charts, star charts, star plots, cobweb charts, irregular polygons
Radar_chart
American mathematician and inventor (1942–2012)
Bases: An Algebraic Resolution of Some Graph Structures, 1975. Advised by Karl Hofmann. *Wallace, David, "Dependence of Multi-Dimensional Array References
David_R._Wallace
Compiler backend for multiple programming languages
and a new graph coloring register allocator.[citation needed] The core of LLVM is the intermediate representation (IR), a low-level programming language
LLVM
Field of mathematics and science based on non-linear systems and initial conditions
result in large differences in a later state (meaning there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly
Chaos_theory
multiple interacting strands is defined by a list of base pairs. A polymer graph for a secondary structure can be constructed by ordering the strands around
NUPACK
Software that translates code from one programming language to another
any compiler optimization. The control-flow graph of every compiled function and the call graph of the program are usually also built during the analysis
Compiler
Optimization algorithms using quantum computing
vertex cover of a graph. The goal here is to find a minimum vertex cover of a graph: a collection of vertices such that each edge in the graph contains at least
Quantum optimization algorithms
Quantum_optimization_algorithms
Generic term for compiler optimization
the size of a compiled program. GCC will move any code upwards or downwards if it "[does not] invalidate any existing dependences nor introduce new ones"
Code_motion
Mathematical inequality relating inner products and norms
extremal graph theory, the Cauchy-Schwarz inequality is used to prove Mantel's theorem, which states that the number of edges in a triangle-free graph on n
Cauchy–Schwarz_inequality
Quantified formulas with real-number variables
problems in geometric graph theory, especially problems of recognizing geometric intersection graphs and straightening the edges of graph drawings with crossings
Existential theory of the reals
Existential_theory_of_the_reals
Statistical distribution for dependence between random variables
uniform on the interval [0, 1]. Copulas are used to describe / model the dependence (inter-correlation) between random variables. Their name, introduced by
Copula_(statistics)
Set of software frameworks for robot software development
package management. Running sets of ROS-based processes are represented in a graph architecture where processing takes place in nodes that may receive, post
Robot_Operating_System
British computer scientist (born 1940)
University of Cambridge. Upton, Eben (2006). Compiling with data dependence graphs (DPhil thesis). University of Cambridge. Cf. British Library catalogue
Martin Richards (computer scientist)
Martin_Richards_(computer_scientist)
Energy policy of the Government of Canada from 1980 to 1985
force, the graph of long-term oil prices shows that prices adjusted for inflation did not drop below pre-1980s levels until 1985. Since the program was cancelled
National_Energy_Program
Algorithmic technique
{\displaystyle k^{2}} edges remain in the graph, and neither of the previous two rules can be applied, then the graph cannot contain a vertex cover of size
Kernelization
Fractal which resembles a plant
Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands
Barnsley_fern
Fixed-value capacitor using ceramic
the electrical dipoles is the reason for the frequency dependence of permittivity. The graph on the right hand side shows typical frequency behavior
Ceramic_capacitor
Semiconductor device with variable capacitance
relationship and a symmetric capacitance-voltage relationship, as shown in the graph to the right. The device was invented by Erik Kollberg together with Anders
Heterostructure barrier varactor
Heterostructure_barrier_varactor
Group of websites that link to each other
In graph-theoretic terms, a link farm is a clique. Although some link farms can be created by hand, most are created through automated programs and services
Link_farm
Context dependence in quantum measurements
better understand contextuality, from the perspective of sheaf theory, graph theory, hypergraphs, algebraic topology, and probabilistic couplings. Nonlocality
Quantum_contextuality
Model in software programming
One is to maintain an explicit dependency graph of the causal dependence relation. Because such a graph can grow arbitrarily large, an event is often
Causal_consistency
Determining what or where each pointer points to in program code
(2000-01-01). "Undecidability of context-sensitive data-dependence analysis". ACM Transactions on Programming Languages and Systems. 22 (1): 162–186. doi:10.1145/345099
Pointer_analysis
Identifier system for audiovisual objects
audiovisual objects, including motion pictures, television, and radio programs. The identification system resolves an identifier to a metadata record
EIDR
Software programming technique
reflection or dynamic programming, hindering IDE automation. Typically requires more upfront development effort. Encourages dependence on a framework. There
Dependency_injection
Ongoing overuse of opioid medication in the US
detox programs. Buprenorphine/naloxone is a combination medication that has been approved by the FDA in 2002 for treatment of opioid dependence. It is
Opioid epidemic in the United States
Opioid_epidemic_in_the_United_States
Method of CPU communication
A003 using its standard memory write instruction. Using the same method, graphs can be displayed on a screen by writing character values into a special
Memory-mapped I/O and port-mapped I/O
Memory-mapped_I/O_and_port-mapped_I/O
Statistical formula
solving a quadratically constrained quadratic program. The first known computable Stein discrepancies were the graph Stein discrepancies (GSDs). Given a discrete
Stein_discrepancy
Diagnostic plot of binary classifier ability
equivalent to sensitivity and FPR is equal to 1 − specificity, the ROC graph is sometimes called the sensitivity vs (1 − specificity) plot. Each prediction
Receiver operating characteristic
Receiver_operating_characteristic
Shortest network connecting points
geometric graphs including the relative neighborhood graph and Delaunay triangulation. By constructing the Delaunay triangulation and then applying a graph minimum
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Sequence of data points over time
mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations
Time_series
PROGRAM DEPENDENCE-GRAPH
PROGRAM DEPENDENCE-GRAPH
Boy/Male
Arabic, Muslim, Sindhi
Dependence; Confidence; Reliance
Boy/Male
Muslim
Way. Program.
Boy/Male
Arabic, Muslim
Way; Program; Road; Path
Boy/Male
Arabic, Armenian, Australian, Indian, Muslim, Parsi, Traditional, Turkish
Free; Independence
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Bird; Independence
Girl/Female
American, Australian, British, Chinese, Christian, English, Latin
Freedom; Independence
Surname or Lastname
English and German
English and German : variant spelling of Pilgrim.
Boy/Male
Arabic
Way; Program
Surname or Lastname
English (mainly Cambridgeshire)
English (mainly Cambridgeshire) : variant of Pilgrim.
Boy/Male
Tamil
Visravas | விஸராவாஸ
Dependence
Visravas | விஸராவாஸ
Boy/Male
Hindu
Dependence
Girl/Female
Assamese, Hindu, Indian, Marathi
Independence
Girl/Female
Tamil
Asritha | அஸà¯à®°à¯€à®¤à®¾
Dependent
Asritha | அஸà¯à®°à¯€à®¤à®¾
Girl/Female
Arabic, Muslim
Reliance; Dependence
Boy/Male
Hebrew
Independence.
Boy/Male
Hebrew
Independence.
Girl/Female
Hindu, Indian
Prowess
Girl/Female
Indian
Dependent
Boy/Male
Hindu, Indian
Start
Boy/Male
Hindu
PROGRAM DEPENDENCE-GRAPH
PROGRAM DEPENDENCE-GRAPH
Boy/Male
Indian
Immortal
Boy/Male
Christian & English(British/American/Australian)
From the Grazing Land
Girl/Female
Australian, Czechoslovakian, Danish, German, Hebrew, Polish
Similar to Alice; Noble; Nobility; God is Perfection; God has Created; God is Zealous; God is My Oath
Female
Hindi/Indian
(अनà¥à¤œà¤¾) Feminine form of Hindi Anuj, ANUJA means "born after; younger."
Boy/Male
Tamil
He who has no imperfections vyanga anywhere in him- the all-perfect. the term vyanga also means person, And so a vyanga means one who cannot be known by anyone in any
Female
English
Latin form of Greek Priskilla, PRISCILLA means "ancient." In the New Testament bible, this is the name of Aquila's wife.
Boy/Male
Muslim
Grace of Allah, Bliss of all
Girl/Female
American, Australian, Biblical, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Hawaiian, Hebrew, Indian, Irish, Jamaican, Jewish, Kannada, Latin, Polish, Swedish
Innocence of a Lamb; Sheep; Ewe; Female Sheep; Little Lamb; One with Purity; Jacob's Wife; Lamb; Gental
Boy/Male
British, English
A Small Bird
Boy/Male
Gaelic
Frank.
PROGRAM DEPENDENCE-GRAPH
PROGRAM DEPENDENCE-GRAPH
PROGRAM DEPENDENCE-GRAPH
PROGRAM DEPENDENCE-GRAPH
PROGRAM DEPENDENCE-GRAPH
n.
One who depends; one who is sustained by another, or who relies on another for support of favor; a hanger-on; a retainer; as, a numerous train of dependents.
a.
Hanging down; as, a dependent bough or leaf.
pl.
of Dependency
n.
That on which one depends or relies; as, he was her sole dependence.
n.
See Programme.
n.
State of being dependent; dependence; state of being subordinate; subordination; concatenation; connection; reliance; trust.
n.
The state or quality of being independent; freedom from dependence; exemption from reliance on, or control by, others; self-subsistence or maintenance; direction of one's own affairs without interference.
n.
Alt. of Dependancy
n.
The act of keeping dependents, or the state of being in dependence.
a.
Dependent on one's self; self-depending; self-reliant.
n.
The act or state of depending; state of being dependent; a hanging down or from; suspension from a support.
n.
That which depends; anything dependent or suspended; anything attached a subordinate to, or contingent on, something else.
n.
An appendage; that which depends on something else, or is distinct from the main dependence; an accessory.
n.
See Dependent, Dependence, Dependency.
a.
Relying on, or subject to, something else for support; not able to exist, or sustain itself, or to perform anything, without the will, power, or aid of something else; not self-sustaining; contingent or conditioned; subordinate; -- often with on or upon; as, dependent on God; dependent upon friends.
n.
A thing hanging down; a dependence.
n.
A territory remote from the kingdom or state to which it belongs, but subject to its dominion; a colony; as, Great Britain has its dependencies in Asia, Africa, and America.
n.
Alt. of Grogran
n.
A dependency; a dependent territory.
n.
Same as Programme.