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A computation tree is a representation for the computation steps of a non-deterministic Turing machine on a specified input. A computation tree is a rooted
Computation_tree
Theory in computer science
Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined;
Computation_tree_logic
Fair computational tree logic is conventional computational tree logic studied with explicit fairness constraints. This declares conditions such as all
Fair_computational_tree_logic
Theoretical model of computation
accept the input. While a DTM has a single "computation path" that it follows, an NTM has a "computation tree". A nondeterministic Turing machine can be
Nondeterministic Turing machine
Nondeterministic_Turing_machine
Probabilistic Computation Tree Logic (PCTL) is an extension of computation tree logic (CTL) that allows for probabilistic quantification of described
Probabilistic_CTL
Mathematical model describing how an output of a function is computed given an input
more specifically in computability theory and computational complexity theory, a model of computation is a model that describes how an output of a mathematical
Model_of_computation
Model of computational complexity
In computational complexity theory, the decision tree model is the model of computation in which an algorithm can be considered to be a decision tree, i
Decision_tree_model
Partition of a simple polygon into triangles
with holes has an Ω(n log n) lower bound, in algebraic computation tree models of computation. It is possible to compute the number of distinct triangulations
Polygon_triangulation
Ability to execute a task in a non-serial manner
concurrent systems. Some of these logics, such as linear temporal logic and computation tree logic, allow assertions to be made about the sequences of states that
Concurrency (computer science)
Concurrency_(computer_science)
Type of temporal logic
branching-time temporal logic that extends computation tree logic (CTL) to multiple players. ATL naturally describes computations of multi-agent systems and concurrent
Alternating-time temporal logic
Alternating-time_temporal_logic
Linked node hierarchical data structure
types of computational trees) This is different from the formal definition of subtree used in graph theory, which is a subgraph that forms a tree – it need
Tree_(abstract_data_type)
System for representing and reasoning about time
were linear temporal logic, a linear-time logic by Amir Pnueli, and computation tree logic (CTL), a branching-time logic by Mordechai Ben-Ari, Zohar Manna
Temporal_logic
American computer scientist (1954–2024)
contributions to temporal logic and modal logic include the introduction of computation tree logic (CTL) and its extension CTL*, which are used in the verification
E._Allen_Emerson
{\displaystyle n} , in a comparison-based model of computation such as a decision tree or algebraic decision tree, is Θ ( n log n ) {\displaystyle \Theta (n\log
Element_distinctness_problem
Tree which includes all vertices of a graph
finding spanning trees in these models of computation. In certain fields of graph theory it is often useful to find a minimum spanning tree of a weighted
Spanning_tree
Tree in formal language theory
parse tree itself is used primarily in computational linguistics; in theoretical syntax, the term syntax tree is more common. Concrete syntax trees reflect
Parse_tree
Notion in combinatorial game theory
(number of leaf nodes in the smallest full-width decision tree for initial position) Computational complexity (asymptotic difficulty of a game as it grows
Game_complexity
a computation tree, minimized over all computation trees that implement the functional. The Kleene–Brouwer order of a well-founded computation tree is
Kleene–Brouwer_order
of computation. Computable topology is not to be confused with algorithmic or computational topology, which studies the application of computation to
Computable_topology
Branch of biology
Computational biology refers to the use of techniques in computer science, data analysis, mathematical modeling and computational simulations to understand
Computational_biology
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
Inherent difficulty of computational problems
theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage
Computational complexity theory
Computational_complexity_theory
Branching-time logic that is a superset of LTL and CTL
CTL* is a superset of computational tree logic (CTL) and linear temporal logic (LTL). It freely combines path quantifiers and temporal operators. Like
CTL*
Self-balancing binary search tree
a WAVL tree or weak AVL tree is a self-balancing binary search tree. WAVL trees are named after AVL trees, another type of balanced search tree, and are
WAVL_tree
Tree connecting given points by short paths
metric geometry and computational geometry, a minimum-diameter spanning tree of a finite set of points in a metric space is a spanning tree in which the diameter
Minimum-diameter spanning tree
Minimum-diameter_spanning_tree
Trial and error problem solvers with a metaheuristic or stochastic optimization character
Evolutionary computation (EC) from computer science is a family of algorithms for global optimization inspired by biological evolution, and a subfield
Evolutionary_computation
Principle in AI development
for pre-LLM models it was often complemented with techniques using computation tree logic. Another common method is theorem proving. Formal verification
Agent_verification
(so-called Markov reward models). CTL: Computation Tree Logic; a branching-time logic, meaning that its model of time is a tree-like structure in which the future
List_of_model_checking_tools
This involves assuming an ordered tree, and reading the accepted/rejected strings from the leaves of the computation tree. NTMs will accept if the leaf string
Leaf_language
Modal temporal logic with modalities referring to time
result known as Kamp's theorem— or equivalently to star-free languages. Computation tree logic (CTL) and linear temporal logic (LTL) are both a subset of CTL*
Linear_temporal_logic
Model used in financial mathematics
The trinomial tree is a lattice-based computational model used in financial mathematics to price options on equity. It was developed by Phelim Boyle in
Trinomial_tree
Complexity class used to classify decision problems
language L. At each of its polynomially many steps, the machine's computation tree branches in at most a finite number of directions. There must be at
NP_(complexity)
language theory, a tree transducer (TT) is an abstract machine taking as input a tree, and generating output – generally other trees, but models producing
Tree_transducer
Computer hardware technology that uses quantum mechanics
that represents and processes information using quantum states. Quantum computations exploit phenomena such as superposition, interference, and entanglement
Quantum_computing
\supseteq } real Abstract interpretation Automated theorem proving Computation tree logic Formal verification List of model checking tools Program analysis
Abstract_model_checking
Transition system
Temporal logic Model checking Kripke semantics Linear temporal logic Computation tree logic Kripke, Saul, 1963, "Semantical Considerations on Modal Logic
Kripke structure (model checking)
Kripke_structure_(model_checking)
Measure of similarity between two graphs
improvements, TED remains computationally expensive for large trees, and its parallelization is highly non-trivial. Specifically, TED computation involves both intra-table
Graph_edit_distance
String that certifies the answer to a computation
decision tree model of computation, certificate complexity is the minimum number of the n {\displaystyle n} input variables of a decision tree that need
Certificate_(complexity)
Shortest network connecting points
spanning tree problem can be established in restricted models of computation. These include the algebraic decision tree and algebraic computation tree models
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Logical problem studied in computer science
reachability, collision detection for convex hulls, minimum cuts, and computation tree logic. Every Datalog program can be interpreted as a monotonic theory
Satisfiability modulo theories
Satisfiability_modulo_theories
Application of computational algorithms, methods and programs to phylogenetic analyses
Computational phylogenetics, phylogeny inference, or phylogenetic inference focuses on computational and optimization algorithms, heuristics, and approaches
Computational_phylogenetics
Branching diagram of evolutionary relationships between organisms
species or taxa. Computational phylogenetics (also phylogeny inference) focuses on the algorithms involved in finding optimal phylogenetic tree in the phylogenetic
Phylogenetic_tree
Type of formal logic
dynamic logic (PDL), (propositional) linear temporal logic (LTL), computation tree logic (CTL), Hennessy–Milner logic, and T.[clarification needed] The
Modal_logic
the 'eventually' (or 'finally') operator found in linear temporal/computation tree logic (branching time logic)(modal logic). So-called branching bisimulation
Stuttering_equivalence
Topics referred to by the same term
Corporation, manufacturer of Chromebooks Certificate Transparency Logs Computation tree logic, a temporal logic Control key, a computer keyboard key CTL timecode
CTL
In computational phylogenetics, tree alignment is a computational problem concerned with producing multiple sequence alignments, or alignments of three
Tree_alignment
Methodic assignment of colors to elements of a graph
based on evaluating this recurrence and the resulting computation tree is sometimes called a Zykov tree. The running time is based on a heuristic for choosing
Graph_coloring
Extension of propositional modal logic
including CTL* and its widely used fragments—linear temporal logic and computational tree logic. An algebraic view is to see it as an algebra of monotonic functions
Modal_μ-calculus
Method in computational phylogenetics
any set of data that are naturally arranged into a tree, but have most applications in computational phylogenetics, especially in maximum parsimony and
Tree_rearrangement
Self-balancing binary search tree data structure
Left-leaning red–black tree AVL tree B-tree (2–3 tree, 2–3–4 tree, B+ tree, B*-tree, UB-tree) Scapegoat tree Splay tree T-tree WAVL tree GNU libavl Cormen
Red–black_tree
State machine for tree structures
A tree automaton is a type of state machine. Tree automata deal with tree structures, rather than the strings of more conventional state machines. The
Tree_automaton
Study of abstract machines and automata
theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical
Automata_theory
which is a tree. A distributed computation which is tree-structured is not uncommon. Such a process graph may arise when the computation is strictly
Dijkstra–Scholten_algorithm
Overview of and topical guide to algorithms
sequence of instructions or rules for solving a problem or performing a computation. Algorithms are central to computer science, mathematics, operations
Outline_of_algorithms
Computer science textbook
The fifth and sixth chapters explore linear temporal logic (LTL) and computation tree logic (CTL), two classes of formula that express properties. LTL encodes
Principles_of_Model_Checking
Numerical method for valuing financial options
or recombine. This property reduces the number of tree nodes, and thus accelerates the computation of the option price. This property also allows the
Binomial options pricing model
Binomial_options_pricing_model
spanning tree (RMST) of a set of n points in the plane (or more generally, in R d {\displaystyle \mathbb {R} ^{d}} ) is a minimum spanning tree of that
Rectilinear minimum spanning tree
Rectilinear_minimum_spanning_tree
Class of algorithms
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting
Tree_traversal
CTI—Computer telephony integration CTFE—Compile-time function execution CTL—Computation tree logic CTM—Close To Metal CTR—Counter mode CTS—Clear to send CTSS—Compatible
List of computing and IT abbreviations
List_of_computing_and_IT_abbreviations
Computer science field
Automated theorem proving Binary decision diagram Büchi automaton Computation tree logic Counterexample-guided abstraction refinement Formal verification
Model_checking
On short connecting nets with added points
Package for computing Steiner trees in the plane: an updated computational study". Mathematical Programming Computation. 10 (4): 487–532. doi:10.1007/s12532-018-0135-8
Steiner_tree_problem
Tree-based computer data structure
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and
B-tree
Subfield of computer science and mathematics
foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory
Theoretical_computer_science
Technique in statistical genetics
1 {\displaystyle D_{1}} tree would be: The second assumption concerns the models of DNA sequence evolution. The computation of the likelihood needs the
Felsenstein's tree-pruning algorithm
Felsenstein's_tree-pruning_algorithm
Formal specification language
Communicating sequential processes Alloy (specification language) B-Method Computation tree logic PlusCal Temporal logic Temporal logic of actions Z notation Lamport
TLA+
Data structure
radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie (prefix tree) in which
Radix_tree
Reimplementation and extension of SMV model checker
ITC-IRST. NuSMV supports the analysis of specifications expressed in computation tree logic (CTL) and linear temporal logic (LTL). It can be run in batch
NuSMV
Multidimensional search tree for points in k dimensional space
approximate nearest neighbor algorithms CGAL the Computational Algorithms Library, has an implementations of k-d tree based nearest neighbor, approximate nearest
K-d_tree
Interactive evolutionary computation (IEC) or aesthetic selection is a general term for methods of evolutionary computation that use human evaluation.
Interactive evolutionary computation
Interactive_evolutionary_computation
of the algorithm in and applied the resulting algorithm to the computation of SPQR-trees. The implementation is publicly available. Chun Ouyang et al.
Program_structure_tree
Machine learning technique
decision tree that approximates the same decision function. Furthermore, its implementation may be more difficult due to the higher computational demand
Gradient_boosting
Proving or disproving the correctness of certain intended algorithms
Language (PSL), SystemVerilog Assertions (SVA),[citation needed] or computational tree logic (CTL). The great advantage of model checking is that it is often
Formal_verification
Complexity class
complement of a regular expression The satisfiability problem for CTL+ (computation tree logic) is 2-EXPTIME-complete. The satisfiability problem of ATL* (alternating-time
2-EXPTIME
Mathematical structure
infinite-tree automaton is a state machine that deals with infinite tree structures. It can be seen as an extension of top-down finite-tree automata to
Infinite-tree_automaton
Mathematical method in graph theory
as the Euler tour representation (ETR) of the tree. The ETT allows for efficient, parallel computation of solutions to common problems in algorithmic
Euler_tour_technique
Network protocol that builds a loop-free logical topology for Ethernet networks
(CBPDU), used for spanning tree computation and sent by root bridges to provide information to all switches. The first Spanning Tree Protocol was invented
Spanning_Tree_Protocol
Concept in model checking (computer science)
they are irrelevant to safety properties. Temporal logics such as computation tree logic (CTL) can be used to specify some LT properties. All linear temporal
Linear_time_property
Combinatorial game theory concept to represent all possible game states
partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated
Game_tree
Decision support tool
specifying actions based on conditions Decision tree model – Model of computational complexity of computation Design rationale – Explicit listing of design
Decision_tree
Mapping of a graph into a tree
solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees, or join trees. They play an important
Tree_decomposition
Convex hull of a finite set of points in a Euclidean space
algebraic decision tree model of computation. The task of computing the volume of a convex polytope has been studied in the field of computational geometry. The
Convex_polytope
Computer science data structure
of the segment tree are in the areas of computational geometry, geographic information systems and machine learning. The segment tree can be generalized
Segment_tree
Evolving computer programs with techniques analogous to natural genetic processes
human-competitive results). Since 2004, the annual Genetic and Evolutionary Computation Conference (GECCO) holds a Human Competitive Awards (called Humies) competition
Genetic_programming
Machine learning algorithm
from data. In data mining, decision trees can be described also as the combination of mathematical and computational techniques to aid the description,
Decision_tree_learning
operation (plus) that be used in a parse tree to do a calculation. 8.2 The PORS Language, Page 215, Evolutionary Computation for Modeling And Optimization - Daniel
PORS
Type of graph in mathematics
c incomparable to each other (also called a diamond-free poset). In computational complexity theory, multitrees have also been called strongly unambiguous
Multitree
Fast Fourier Transform algorithm
the explicit recursion is avoided, and instead one traverses the computational tree in breadth-first fashion. The above re-expression of a size-N DFT
Cooley–Tukey_FFT_algorithm
Directed graph with no directed cycles
and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling)
Directed_acyclic_graph
Weighted tree representing s-t cuts of a graph
for all s-t pairs in the graph. The Gomory–Hu tree can be constructed in |V| − 1 maximum flow computations. It is named for Ralph E. Gomory and T. C. Hu
Gomory–Hu_tree
Ability of a computing system to simulate Turing machines
model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal
Turing_completeness
Tree node with two other nodes as descendants
w to the root. In general, the computational time required for this algorithm is O(h) where h is the height of the tree (length of longest path from a
Lowest_common_ancestor
On the number of spanning trees in a graph
theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph. It states that this number can be
Kirchhoff's_theorem
Way of representing the hierarchical nature of a structure in a graphical form
Peter Eades, Tao Lin, and Xuemin Lin, "Two Tree Drawing Conventions", International Journal of Computational Geometry and Applications, 1993, volume 3
Tree_structure
Heuristic search algorithm for evaluating game trees
(2008). "Progressive Strategies for Monte-Carlo Tree Search" (PDF). New Mathematics and Natural Computation. 4 (3): 343–359. doi:10.1142/s1793005708001094
Monte_Carlo_tree_search
Sequence of operations for a task
typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and
Algorithm
Chart representing family relationships
demonstrates a novel computational method for estimating how human DNA is related via a series of 13 million linked trees along the genome, a tree-sequence,[clarification
Family_tree
Israeli–New Zealand bioinformatician (1961–2025)
method's computational performance and statistical accuracy against competing approaches. Related work extended the multispecies coalescent to gene tree simulation
Joseph_Heled
Set of all Pareto efficient situations
Evolutionary Algorithms Since generating the entire Pareto front is often computationally-hard, there are algorithms for computing an approximate Pareto-front
Pareto_front
Static code analysis tool
domain specific language for abstract syntax tree linting, based on ideas from model checking for computation tree logic. Infer is mostly written in the OCaml
Infer_Static_Analyzer
with tree-walking automata. For a different notion of tree automaton, closely related to regular tree languages, see branching automaton. All trees are
Tree-walking_automaton
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