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E-graph
In computer science, an e-graph is a data structure that stores an equivalence relation over terms of some language. Definition and operations Let \Sigma be a set of uninterpreted functions, where \Sigma_n is the subset of \Sigma consisting of functions of arity n. Let \mathbb be a countable set of opaque identifiers that may be compared for equality, called e-class IDs. The application of f\in\Sigma_n to e-class IDs i_1, i_2, \ldots, i_n\in\mathbb is denoted f(i_1, i_2, \ldots, i_n) and called an e-node. The e-graph then represents equivalence classes of e-nodes, using the following data structures: * A union-find structure U representing equivalence classes of e-class IDs, with the usual operations \mathrm, \mathrm and \mathrm. An e-class ID e is canonical if \mathrm(U, e) = e; an e-node f(i_1,\ldots,i_n) is canonical if each i_j is canonical (j in 1,\ldots,n). * An association of e-class IDs with sets of e-nodes, called e-classes. This consists of ** a hashcons H (i.e. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Syntax Tree
An abstract syntax tree (AST) is a data structure used in computer science to represent the structure of a program or code snippet. It is a tree representation of the abstract syntactic structure of text (often source code) written in a formal language. Each node of the tree denotes a construct occurring in the text. It is sometimes called just a syntax tree. The syntax is "abstract" in the sense that it does not represent every detail appearing in the real syntax, but rather just the structural or content-related details. For instance, grouping parentheses are implicit in the tree structure, so these do not have to be represented as separate nodes. Likewise, a syntactic construct like an if-condition-then statement may be denoted by means of a single node with three branches. This distinguishes abstract syntax trees from concrete syntax trees, traditionally designated parse trees. Parse trees are typically built by a parser during the source code translation and compiling pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LLVM
LLVM, also called LLVM Core, is a target-independent optimizer and code generator. It can be used to develop a Compiler#Front end, frontend for any programming language and a Compiler#Back end, backend for any instruction set architecture. LLVM is designed around a language-independent specification, language-independent intermediate representation (IR) that serves as a Software portability, portable, high-level assembly language that can be optimizing compiler, optimized with a variety of transformations over multiple passes. The name ''LLVM'' originally stood for ''Low Level Virtual Machine.'' However, the project has since expanded, and the name is no longer an acronym but an orphan initialism. LLVM is written in C++ and is designed for compile-time, Linker (computing), link-time, runtime (program lifecycle phase), runtime, and "idle-time" optimization. Originally implemented for C (programming language), C and C++, the language-agnostic design of LLVM has since spawned a wide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Translation Validation
In computing, compiler correctness is the branch of computer science that deals with trying to show that a compiler In computing, a compiler is a computer program that Translator (computing), translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primaril ... behaves according to its programming language, language specification. Techniques include developing the compiler using formal methods and using rigorous testing (often called compiler validation) on an existing compiler. Formal verification Two main formal verification approaches for establishing correctness of compilation are proving correctness of the compiler for all inputs and proving correctness of a compilation of a particular program (translation validation). Compiler correctness for all input programs Compiler validation with formal methods involves a long chain of formal, deductive logic. However, since ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathematics), matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as line (geometry), lines, plane (geometry), planes and rotation (mathematics), rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to Space of functions, function spaces. Linear algebra is also used in most sciences and fields of engineering because it allows mathematical model, modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deep Learning
Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be either supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimizing Compiler
An optimizing compiler is a compiler designed to generate code that is optimized in aspects such as minimizing program execution time, memory usage, storage size, and power consumption. Optimization is generally implemented as a sequence of optimizing transformations, a.k.a. compiler optimizations algorithms that transform code to produce semantically equivalent code optimized for some aspect. Optimization is limited by a number of factors. Theoretical analysis indicates that some optimization problems are NP-complete, or even undecidable. Also, producing perfectly ''optimal'' code is not possible since optimizing for one aspect often degrades performance for another. Optimization is a collection of heuristic methods for improving resource usage in typical programs. Categorization Local vs. global scope Scope describes how much of the input code is considered to apply optimizations. Local scope optimizations use information local to a basic block. Since basic blocks cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ESC/Java
ESC/Java (and more recently ESC/Java2), the "Extended Static Checker for Java," is a programming tool that attempts to find common run-time errors in Java programs at compile time. The underlying approach used in ESC/Java is referred to as extended static checking, which is a collective name referring to a range of techniques for statically checking the correctness of various program constraints. For example, that an integer variable is greater-than-zero, or lies between the bounds of an array. This technique was pioneered in ESC/Java (and its predecessor, ESC/Modula-3) and can be thought of as an extended form of type checking. Extended static checking usually involves the use of an automated theorem prover and, in ESC/Java, the Simplify theorem prover was used. ESC/Java is neither sound nor complete. This was intentional and aims to reduce the number of errors and/or warnings reported to the programmer, in order to make the tool more useful in practice. However, it does ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conflict-driven Clause Learning
In computer science, conflict-driven clause learning (CDCL) is an algorithm for solving the Boolean satisfiability problem (SAT). Given a Boolean formula, the SAT problem asks for an assignment of variables so that the entire formula evaluates to true. The internal workings of CDCL SAT solvers were inspired by DPLL solvers. The main difference between CDCL and DPLL is that CDCL's backjumping is non-chronological. Conflict-driven clause learning was proposed by Marques-Silva and Karem A. Sakallah (1996, 1999) and Bayardo and Schrag (1997). Background Boolean satisfiability problem The satisfiability problem consists in finding a satisfying assignment for a given formula in conjunctive normal form (CNF). An example of such a formula is: :( ( not ''A'') or (not ''C'') ) and (''B'' or ''C''), or, using a common notation:In the pictures below, "+" is used to denote "or", multiplication to denote "and", and a postfix "'" to denote "not". :(\lnot A \lor \lnot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DPLL(T)
In computer science, DPLL(T) is a framework for determining the satisfiability of SMT problems. The algorithm extends the original SAT-solving DPLL algorithm with the ability to reason about an arbitrary theory ''T''. At a high level, the algorithm works by transforming an SMT problem into a SAT formula where atoms are replaced with Boolean variables. The algorithm repeatedly finds a satisfying valuation for the SAT problem, consults a theory solver to check consistency under the domain-specific theory, and then (if a contradiction is found) refines the SAT formula with this information. Many modern SMT solvers, such as Microsoft's Z3 Theorem Prover and CVC4 In computer science and mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are CVC4 and CVC5 (stylized cvc5); earlier versions include CVC, CVC Li ..., use DPLL(T) to power their core solving capabilities. References A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty Theory
In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and '' n-ary'' form. Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational theories. The satisfiability problem for free theories is solved by syntactic unification; algorithms for the latter are used by interpreters for various computer languages, such as Prolog. Syntactic unification is also used in algorithms for the satisfiability problem for certain other equational theories, see Unification (computer science). Example As an example of uninterpreted functions for SMT-LIB, if this input is given to an SMT solver: (declare-fun f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CVC4
In computer science and mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are CVC4 and CVC5 (stylized cvc5); earlier versions include CVC, CVC Lite, and CVC3. Both CVC4 and cvc5 support the SMT-LIB and TPTP input formats for solving SMT problems, and the SyGuS-IF format for program synthesis. Both CVC4 and cvc5 can output proofs that can be independently checked in the LFSC format, cvc5 additionally supports the Alethe and Lean 4 formats. cvc5 has bindings for C++, Python, and Java. CVC4 competed in SMT-COMP in the years 2014-2020, and cvc5 has competed in the years 2021-2022. CVC4 competed in SyGuS-COMP in the years 2015-2019, and in CASC in 2013-2015. CVC4 uses the DPLL(T) architecture, and supports the theories of linear arithmetic over rationals and integers, fixed-width bitvectors, floating-point arithmetic, strings, (co)-datatypes, sequences (used to model dynamic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
