Algorithmic probability

In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s. It is used in inductive inference theory and analyses of algorithms. In his general theory of inductive inference, Solomonoff uses the method together with Bayes' rule to obtain probabilities of prediction for an algorithm's future outputs. In the mathematical formalism used, the observations have the form of finite binary strings viewed as outputs of Turing machines, and the universal prior is a probability distribution over the set of finite binary strings calculated from a probability distribution over programs (that is, inputs to a universal Turing machine). The prior is universal in the Turing-computability sense, i.e. no string has zero probability. It is not computable, but it can be approximated. Formally, the probability P {\displaystyle P} is not a probability and it is not computable. It is only "lower semi-computable" and a "semi-measure". By "semi-measure", it means that 0 ≤ ∑ x P ( x ) < 1 {\displaystyle 0\leq \sum _{x}P(x)<1} . That is, the "probability" does not actually sum up to one, unlike actual probabilities. This is because some inputs to the Turing machine causes it to never halt, which means the probability mass allocated to those inputs is lost. By "lower semi-computable", it means there is a Turing machine that, given an input string x {\displaystyle x} , can print out a sequence y 1 < y 2 < ⋯ {\displaystyle y_{1}

N-World

N-World is a 3D graphics package developed by Nichimen Graphics in the 1990s, for Silicon Graphics and Windows NT workstations. Intended primarily for video game content creation, it has polygon modeling tools, 2D and 3D paint, scripting, color reduction, and exporters for several popular game consoles. After its initial release on Windows NT, N-World was renamed Mirai. The winged edge 3D modeler in N-World inspired the development at Nichimen Graphics of Nendo, a standalone 3D modeler, which in turn inspired the open source modeler Wings 3D. == History == N-World originated with Symbolics, a computer manufacturer notable for producing Lisp-based systems in the 1980s. Among the software packages that were produced for Symbolics computers are S-Graphics, a 3D animation suite that includes modules for polygon modeling, dynamics, paint, and rendering — titled S-Geometry, S-Dynamics, S-Paint, and S-Render, respectively. In 1992, Japanese trading company Nichimen Corporation purchased the rights to S-Graphics, ported it to Silicon Graphics IRIX, and marketed it as N-World. N-World retains the Lisp-based underpinnings of its predecessor, but was targeted at interactive content producers, with features useful for game developers. It was priced at US$16,995 (equivalent to $34,100 in 2025) for the full suite, later reduced to $9,995 when ported to Windows NT in 1997. N-World was used to create graphics for many console games in the 1990s, specifically most of the Nintendo 64 games, like Super Mario 64 and Final Fantasy VII. It was superseded by Mirai in 1999. == Features == The N-World package, like its predecessor S-Graphics, is divided into several components: N-Geometry: 3D polygon-based modeling tools, including smoothing, "magnet" geometry editing, and instancing. N-Dynamics: Animation tools including scripting, curve-based animation, and skeletal animation. N-Render: Surfacing and rendering tools with ray tracing and materials output to various game console formats. N-Paint: 2D and 3D paint with mattes, effects, color reduction, and a visual VRAM editor for PlayStation. Game Tools: Utilities for game developers, including exporters for PlayStation, Nintendo 64, and Saturn consoles. == Credits == The following games were created using N-World. Rap Stars Online

Timeline of operating systems

This article presents a timeline of events in the history of computer operating systems from 1951 to the current day. For a narrative explaining the overall developments, see the History of operating systems. == 20th Century == == 1940s == 1949 EDSAC was considered the first operating system developed by Maurice Wilkes and manufactured by the University of Cambridge == 1950s == 1951 LEO I 'Lyons Electronic Office' was the commercial development of EDSAC computing platform, supported by British firm J. Lyons and Co. 1953 DYSEAC - an early machine capable of distributing computing 1955 General Motors Operating System made for IBM 701 MIT's Tape Director operating system made for UNIVAC 1103 1956 GM-NAA I/O for IBM 704, based on General Motors Operating System 1957 Atlas Supervisor (Manchester University) (Atlas computer project start) BESYS (Bell Labs), for IBM 704, later IBM 7090 and IBM 7094 1958 University of Michigan Executive System (UMES), for IBM 704, 709, and 7090 1959 SHARE Operating System (SOS), based on GM-NAA I/O == 1960s == 1960 IBSYS (IBM for its 7090 and 7094) 1961 CTSS demonstration (MIT's Compatible Time-Sharing System for the IBM 7094) MCP (Burroughs Master Control Program) for B5000 1962 Atlas Supervisor (Manchester University) (Atlas computer commissioned) BBN Time-Sharing System GCOS (GE's General Comprehensive Operating System, originally GECOS, General Electric Comprehensive Operating Supervisor) 1963 ADMIRAL AN/FSQ-32, another early time-sharing system begun CTSS becomes operational (MIT's Compatible Time-Sharing System for the IBM 7094) JOSS, an interactive time-shared system that did not distinguish between operating system and language Titan Supervisor, early time-sharing system begun 1964 Berkeley Timesharing System (for Scientific Data Systems' SDS 940) Chippewa Operating System (for CDC 6600 supercomputer) Dartmouth Time-Sharing System (Dartmouth College's DTSS for GE computers) EXEC 8 (UNIVAC) KDF9 Timesharing Director (English Electric) – an early, fully hardware secured, fully pre-emptive process switching, multi-programming operating system for KDF9 (originally announced in 1960) OS/360 (IBM's primary OS for its S/360 series) (announced) PDP-6 Monitor (DEC) descendant renamed TOPS-10 in 1970 SCOPE (CDC 3000 series) 1965 BOS/360 (IBM's Basic Operating System) DECsys TOS/360 (IBM's Tape Operating System) Livermore Time Sharing System (LTSS) Multics (MIT, GE, Bell Labs for the GE-645) (announced) Pick operating system SIPROS 66 (Simultaneous Processing Operating System) THE multiprogramming system (Technische Hogeschool Eindhoven) development TSOS (later VMOS) (RCA) 1966 DOS/360 (IBM's Disk Operating System) GEORGE 1 & 2 for ICT 1900 series Mod 1 Mod 2 Mod 8 MS/8 (Richard F. Lary's DEC PDP-8 system) MSOS (Mass Storage Operating System) OS/360 (IBM's primary OS for its S/360 series) PCP and MFT (shipped) RAX Remote Users of Shared Hardware (RUSH), a time-sharing system developed by Allen-Babcock for the IBM 360/50 SODA for Elwro's Odra 1204 Universal Time-Sharing System (XDS Sigma series) 1967 CP-40, predecessor to CP-67 on modified IBM System/360 Model 40 CP-67 (IBM, also known as CP/CMS) Conversational Programming System (CPS), an IBM time-sharing system under OS/360 Michigan Terminal System (MTS) (time-sharing system for the IBM S/360-67 and successors) ITS (MIT's Incompatible Timesharing System for the DEC PDP-6 and PDP-10) OS/360 MVT ORVYL (Stanford University's time-sharing system for the IBM S/360-67) TSS/360 (IBM's Time-sharing System for the S/360-67, never officially released, canceled in 1969 and again in 1971) WAITS (SAIL, Stanford Artificial Intelligence Laboratory, time-sharing system for DEC PDP-6 and PDP-10, later TOPS-10) 1968 Airline Control Program (ACP) (IBM) B1 (NCR Century series) CALL/360, an IBM time-sharing system for System/360 HP Real-Time Executive (HP RTE) – Hewlett-Packard HP Time-Shared BASIC (HP TSB) – Hewlett-Packard (time-sharing system for the HP 2000) THE multiprogramming system (Eindhoven University of Technology) publication TSS/8 (DEC for the PDP-8) VP/CSS 1969 B2 (NCR Century series) B3 (NCR Century series) GEORGE 3 For ICL 1900 series MINIMOP Multics (MIT, GE, Bell Labs for the GE-645 and later the Honeywell 6180) (opened for paying customers in October) RC 4000 Multiprogramming System (RC) TENEX (Bolt, Beranek and Newman for DEC systems, later TOPS-20) Unics (later Unix) (AT&T, initially on DEC computers) Xerox Operating System == 1970s == 1970 DOS-11 (PDP-11) 1971 EMAS Kronos RSTS-11 2A-19 (First released version; PDP-11) RSX-15 OS/8 1972 B4 (NCR Century series) COS-300 Data General RDOS Edos MUSIC/SP OS/4 OS 1100 OS/2000 (Honeywell 2000-series) Operating System/Virtual Storage 1 (OS/VS1) Operating System/Virtual Storage 2 R1 (OS/VS2 SVS) PRIMOS (written in FORTRAN IV, that didn't have pointers, while later versions, around version 18, written in a version of PL/I, called PL/P) Virtual Machine/Basic System Extensions Program Product (BSEPP or VM/SE) Virtual Machine/System Extensions Program Product (SEPP or VM/BSE) Virtual Machine Facility/370 (VM/370), sometimes known as VM/CMS 1973 Эльбрус-1 (Elbrus-1) – Soviet computer – created using high-level language uЭль-76 (AL-76/ALGOL 68) Alto OS CP-V (Control Program V) RSX-11D RT-11 VME – implementation language S3 (ALGOL 68) 1974 ACOS-2 (NEC) ACOS-4 ACOS-6 CP/M DOS-11 V09-20C (Last stable release, June 1974) Hydra – capability-based, multiprocessing OS kernel MONECS Multi-Programming Executive (MPE) – Hewlett-Packard Operating System/Virtual Storage 2 R2 (MVS) OS/7 OS/16 OS/32 Sintran III 1975 BS2000 V2.0 (First released version) COS-350 ISIS NOS (Control Data Corporation) OS/3 (Univac) VS/9 (formerly RCA's TSOS, later named VMOS) Version 6 Unix XVM/DOS XVM/RSX 1976 Cambridge CAP computer – all operating system procedures written in ALGOL 68C, with some closely associated protected procedures in BCPL Cray Operating System DX10 FLEX TOPS-20 TX990/TXDS Tandem Nonstop OS v1 Thoth 1977 1BSD AMOS KERNAL OASIS operating system OS68 OS4000 RMX-80 System 88 (Exec) System Support Program (IBM System/34 and System/36) TRSDOS Virtual Memory System (VMS) V1.0 (Initial commercial release, October 25) VRX (Virtual Resource eXecutive) VS Virtual Memory Operating System 1978 2BSD Apple DOS Control Program Facility (IBM System/38) Cray Time Sharing System (CTSS) DPCX (IBM) DPPX (IBM) HDOS KSOS – secure OS design from Ford Aerospace KVM/370 – security retro-fit of IBM VM/370 Lisp machine (CADR) MVS/System Extensions (MVS/SE) OS4 (Naked Mini 4) PTDOS TRIPOS UCSD p-System (First released version) Z80-RIO 1979 Atari DOS 3BSD CP-6 Idris MP/M MVS/System Extensions R2 (MVS/SE2) NLTSS POS Sinclair BASIC Transaction Processing Facility (TPF) (IBM) UCLA Secure UNIX – an early secure UNIX OS based on security kernel UNIX/32V DOS/VSE Version 7 Unix == 1980s == 1980 86-DOS AOS/VS (Data General) Business Operating System CTOS DOSPLUS (TRS-80) MVS/System Product (MVS/SP) V1 NewDos/80 OS-9 RMX-86 RS-DOS SOS Virtual Machine/System Product (VM/SP) Xenix 1981 Acorn MOS Aegis SR1 (First Apollo/DOMAIN systems shipped on March 27) CP/M-86 DRX (Distributed Resource Executive) iMAX – OS for Intel's iAPX 432 capability machine MCS (Multi-user Control System) MS-DOS PC DOS Pilot (Xerox Star operating system) UNOS UTS V VERSAdos VRTX VSOS (Virtual Storage Operating System) Xinu first release 1982 Commodore DOS LDOS (By Logical Systems, Inc. – for the Radio Shack TRS-80 Models I, II & III) PCOS (Olivetti M20) pSOS QNX Stratus VOS Sun UNIX (later SunOS) 0.7 Ultrix Unix System III VAXELN 1983 Coherent DNIX EOS GNU (project start) Lisa Office System 7/7 LOCUS – UNIX compatible, high reliability, distributed OS MVS/System Product V2 (MVS/Extended Architecture, MVS/XA) Novell NetWare (S-Net) PERPOS ProDOS RTU (Real-Time Unix) STOP – TCSEC A1-class, secure OS for SCOMP hardware SunOS 1.0 VSE/System Package (VSE/SP) Version 1 1984 AMSDOS CTIX (Unix variant) DYNIX Mac OS (System 1.0) MSX-DOS NOS/VE PANOS PC/IX ROS Sinclair QDOS SINIX UNICOS Venix 2.0 Virtual Machine/Extended Architecture Migration Assistance (VM/XA MA) 1985 AmigaOS Atari TOS DG/UX DOS Plus Graphics Environment Manager Harmony MacOS 2 MIPS RISC/os Oberon – written in Oberon SunOS 2.0 Version 8 Unix Virtual Machine/Extended Architecture System Facility (VM/XA SF) Windows 1.0 Windows 1.01 Xenix 2.0 1986 AIX 1.0 Cronus distributed OS FlexOS GEMSOS – TCSEC A1-class, secure kernel for BLACKER VPN & GTNP GEOS Genera 7.0 HP-UX MacOS 3 SunOS 3.0 TR-DOS TRIX Version 9 Unix 1987 Arthur (much improved version came in 1989 under the name RISC OS) BS2000 V9.0 IRIX (3.0 is first SGI version) MacOS 4 MacOS 5 MDOS MINIX 1.0 OS/2 (1.0) PC-MOS/386 Topaz – semi-distributed OS for DEC Firefly workstation written in Modula-2+ and garbage collected VxWorks Windows 2.0 1988 A/UX (Apple Computer) AOS/VS II (Data General) CP/M rebranded as DR-DOS Flex machine – tagged, capability machine with OS and other software written

Asymmetric follow

An asymmetric follow social network is one which allows many people to follow an individual or account without having to follow them back. It is also known as asynchronous follow or sometimes asymmetric friendship. Asymmetric follow is a common pattern on Twitter, where someone may have thousands of followers, but themselves follow few (or no) accounts. In September 2010 Facebook started experimenting with a similar feature, which Facebook calls "Subscribe To."

Digital first

Digital first is a communication theory that publishers should release content into new media channels in preference to old media. The premise behind the theory is that after the advent of Internet, most established media organizations continued to give priority to traditional media. Over time, those organizations faced a choice to either publish first in digital media or traditional media. A "digital first" decision occurs when a publisher chooses to distribute information online in preference to or at the expense of traditional media like print publishing. Many employers and employees find it challenging to imagine using digital first practices. Distributing content digital first introduces new practices, including a need to manage the data which tracks readership. Many paper print publishers feel intimidated by the idea of publishing content online before publishing it in paper media. Comedian John Oliver in the show Last Week Tonight criticized digital first practices as a cause of lower standards in journalism. == Digital-First Transformation in Business and Education == The classical perspective of an information system is that it represents and reflects physical reality. However, it is increasingly evident that digital technologies not only represent reality but also actively shape it, as, in many instances, the digital version is created first, and the physical version follows. Gradually, digital infrastructures are integrated in people's work and life, shaping a digital environment through technologies such as 5G, sensors, and blockchain. The Digital First Framework, developed by Professor Youngjin Yoo, is a conceptual approach that helps the physical companies in the integration of digital technologies into the core of product and service design. The shift from traditional cars, where the physical vehicle precedes its digital representation on Google maps, to autonomous vehicles, where the digital representation (the blue dot) is created first, emphasizes the digital-first mindset in the design and operation of systems. In today's business environment, it's critical for organizations to embrace a digital-first strategy. Companies built on digital platforms will significantly diverge from traditional, hierarchical business structures that typically focus on a single product or market. These digitally-centered enterprises will offer products and services that are tailored to individual requirements, utilizing algorithms to assess needs based on specific situations, and relying on external partners to provide these solutions. This highlights the need to transform traditional R&D practices. It's essential for R&D teams to move beyond their laboratories and immerse themselves in the environments of their users. Understanding the context of use is fundamental to creating a relevant platform. As an illustration, the concept of Digital-first, as defined by Rohm et al. (2019), involves the integration of digital projects within educational courses, exemplified by institutions like M-School. The program adopts a programmatic approach, where successive courses progressively build upon one another, adopting an all-encompassing perspective that regards all aspects of marketing as inherently digital. Students actively participate in real-world projects, including campaigns for community improvement, and are tasked with generating content for diverse platforms. Through hands-on collaboration with live clients and the utilization of tools such as Google AdWords and Facebook Advertising, students acquire practical experience in the realms of digital marketing and analytics. == vBook == A vBook is an eBook that is digital first media with embedded video, images, graphs, tables, text, and other media.

Neighborhood operation

In computer vision and image processing a neighborhood operation is a commonly used class of computations on image data which implies that it is processed according to the following pseudo code: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N) } This general procedure can be applied to image data of arbitrary dimensionality. Also, the image data on which the operation is applied does not have to be defined in terms of intensity or color, it can be any type of information which is organized as a function of spatial (and possibly temporal) variables in p. The result of applying a neighborhood operation on an image is again something which can be interpreted as an image, it has the same dimension as the original data. The value at each image point, however, does not have to be directly related to intensity or color. Instead it is an element in the range of the function f, which can be of arbitrary type. Normally the neighborhood N is of fixed size and is a square (or a cube, depending on the dimensionality of the image data) centered on the point p. Also the function f is fixed, but may in some cases have parameters which can vary with p, see below. In the simplest case, the neighborhood N may be only a single point. This type of operation is often referred to as a point-wise operation. == Examples == The most common examples of a neighborhood operation use a fixed function f which in addition is linear, that is, the computation consists of a linear shift invariant operation. In this case, the neighborhood operation corresponds to the convolution operation. A typical example is convolution with a low-pass filter, where the result can be interpreted in terms of local averages of the image data around each image point. Other examples are computation of local derivatives of the image data. It is also rather common to use a fixed but non-linear function f. This includes median filtering, and computation of local variances. The Nagao-Matsuyama filter is an example of a complex local neighbourhood operation that uses variance as an indicator of the uniformity within a pixel group. The result is similar to a convolution with a low-pass filter with the added effect of preserving sharp edges. There is also a class of neighborhood operations in which the function f has additional parameters which can vary with p: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N, parameters(p)) } This implies that the result is not shift invariant. Examples are adaptive Wiener filters. == Implementation aspects == The pseudo code given above suggests that a neighborhood operation is implemented in terms of an outer loop over all image points. However, since the results are independent, the image points can be visited in arbitrary order, or can even be processed in parallel. Furthermore, in the case of linear shift-invariant operations, the computation of f at each point implies a summation of products between the image data and the filter coefficients. The implementation of this neighborhood operation can then be made by having the summation loop outside the loop over all image points. An important issue related to neighborhood operation is how to deal with the fact that the neighborhood N becomes more or less undefined for points p close to the edge or border of the image data. Several strategies have been proposed: Compute result only for points p for which the corresponding neighborhood is well-defined. This implies that the output image will be somewhat smaller than the input image. Zero padding: Extend the input image sufficiently by adding extra points outside the original image which are set to zero. The loops over the image points described above visit only the original image points. Border extension: Extend the input image sufficiently by adding extra points outside the original image which are set to the image value at the closest image point. The loops over the image points described above visit only the original image points. Mirror extension: Extend the image sufficiently much by mirroring the image at the image boundaries. This method is less sensitive to local variations at the image boundary than border extension. Wrapping: The image is tiled, so that going off one edge wraps around to the opposite side of the image. This method assumes that the image is largely homogeneous, for example a stochastic image texture without large textons.

Digital signal

A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within an infinite set of values. Simple digital signals represent information in discrete bands of levels. All levels within a band of values represent the same information state. In most digital circuits, the signal can have two possible valid values; this is called a binary signal or logic signal. They are represented by two voltage bands: one near a reference value (typically termed as ground or zero volts), and the other a value near the supply voltage. These correspond to the two values zero and one (or false and true) of the Boolean domain, so at any given time a binary signal represents one binary digit (bit). Because of this discretization, relatively small changes to the signal levels do not leave the discrete envelope, and as a result are ignored by signal state sensing circuitry. As a result, digital signals have noise immunity; electronic noise, provided it is not too great, will not affect digital circuits, whereas noise always degrades the operation of analog signals to some degree. Digital signals having more than two states are occasionally used; circuitry using such signals is called multivalued logic. For example, signals that can assume three possible states are called three-valued logic. In a digital signal, the physical quantity representing the information may be a variable electric current or voltage, the intensity, phase or polarization of an optical or other electromagnetic field, acoustic pressure, the magnetization of a magnetic storage media, etcetera. Digital signals are used in all digital electronics, notably computing equipment and data transmission. == Definitions == The term digital signal has related definitions in different contexts. === In digital electronics === In digital electronics, a digital signal is a pulse amplitude modulated signal, i.e., a sequence of fixed-width electrical pulses or light pulses, each occupying one of a discrete number of levels of amplitude. A special case is a logic signal or a binary signal, which varies between a low and a high signal level. The pulse trains in digital circuits are typically generated by metal–oxide–semiconductor field-effect transistor (MOSFET) devices, due to their rapid on–off electronic switching speed and large-scale integration (LSI) capability. In contrast, bipolar junction transistors more slowly generate signals resembling sine waves. === In signal processing === In digital signal processing, a digital signal is a representation of a physical signal that is sampled and quantized. A digital signal is an abstraction that is discrete in time and amplitude. The signal's value only exists at regular time intervals, since only the values of the corresponding physical signal at those sampled moments are significant for further digital processing. The digital signal is a sequence of codes drawn from a finite set of values. The digital signal may be stored, processed or transmitted physically as a pulse-code modulation (PCM) signal. === In communications === In digital communications, a digital signal is a continuous-time physical signal, alternating between a discrete number of waveforms, representing a bitstream. The shape of the waveform depends on the transmission scheme, which may be either a line coding scheme allowing baseband transmission; or a digital modulation scheme, allowing passband transmission over long wires or over a limited radio frequency band. Such a carrier-modulated sine wave is considered a digital signal in literature on digital communications and data transmission, but considered as a bit stream converted to an analog signal in specific cases where the signal will be carried over a system meant for analog communication, such as an analog telephone line. In communications, sources of interference are usually present, and noise is frequently a significant problem. The effects of interference are typically minimized by filtering off interfering signals as much as possible and by using data redundancy. The main advantages of digital signals for communications are often considered to be noise immunity, and the ability, in many cases such as with audio and video data, to use data compression to greatly decrease the bandwidth that is required on the communication media. == Logic voltage levels == A waveform that switches representing the two states of a Boolean value (0 and 1, or low and high, or false and true) is referred to as a digital signal or logic signal or binary signal when it is interpreted in terms of only two possible digits. The two states are usually represented by some measurement of an electrical property: Voltage is the most common, but current is used in some logic families. Two ranges of voltages are typically defined for each logic family, which are frequently not directly adjacent. The signal is low when in the low range and high when in the high range, and in between the two ranges the behavior can vary between different types of gates. The clock signal is a special digital signal that is used to synchronize many digital circuits. The image shown can be considered the waveform of a clock signal. Logic changes are triggered either by the rising edge or the falling edge. The rising edge is the transition from a low voltage (level 1 in the diagram) to a high voltage (level 2). The falling edge is the transition from a high voltage to a low one. Although in a highly simplified and idealized model of a digital circuit, we may wish for these transitions to occur instantaneously, no real-world circuit is purely resistive, and therefore no circuit can instantly change voltage levels. This means that during a short, finite transition time, the output may not properly reflect the input, and will not correspond to either a logically high or low voltage. == Modulation == To create a digital signal, a signal must be modulated with a control signal to produce it. The simplest modulation, a type of unipolar encoding, is simply to switch on and off a DC signal so that high voltages represent a '1' and low voltages are '0'. In digital radio schemes, one or more carrier waves are amplitude, frequency or phase modulated by the control signal to produce a digital signal suitable for transmission. Asymmetric Digital Subscriber Line (ADSL) over telephone wires, does not primarily use binary logic; the digital signals for individual carriers are modulated with different-valued logics, depending on the Shannon capacity of the individual channel. == Clocking == Digital signals may be sampled by a clock signal at regular intervals by passing the signal through a flip-flop. When this is done, the input is measured at the clock edge and the signal from that time. The signal is then held steady until the next clock. This process is the basis of synchronous logic. Asynchronous logic also exists, which uses no single clock, and generally operates more quickly, and may use less power, but is significantly harder to design.