Separating Words Problem

*</plaintext></div> <script src="/js/AdvertTop1.js"> </script> <center> </center> <br> <center> <form id="newForm" target="_top" method="post" action="/php/HTMLGet.php"> <input type="text" name="FindGo" style=" width:410; px;height:40px; font-size:14pt;"> <input type="submit" value="Find" style=" width:80 px;height:40px; font-size:14pt;"> </form> </center> <br> <font size=1>     <br> <div class="list-text" id="list-text"> <table style="width:100%"> <tr; > <td width="15%"><p> <a href="/html/ALL/s/S/Separating_Words_Problem.html" title="Click for more on -> Separating Words Problem"> <span><br><div><script src="/js/AdvertListPict.js"></script></div><br></span> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/S/Separating_Words_Problem.html" style="text-decoration:none;">Separating Words Problem</a></b></big></big><br> In theoretical computer science, the separating words problem is the problem of finding the smallest deterministic finite automaton that behaves differently on two given strings, meaning that it accepts one of the two strings and rejects the other string. It is an open problem how large such an automaton must be, in the worst case, as a function of the length of the input strings. Example The two strings 0010 and 1000 may be distinguished from each other by a three-state automaton in which the transitions from the start state go to two different states, both of which are terminal in the sense that subsequent transitions from these two states always return to the same state. The state of this automaton records the first symbol of the input string. If one of the two terminal states is accepting and the other is rejecting, then the automaton will accept only one of the strings 0010 and 1000. However, these two strings cannot be distinguished by any automaton with fewer than three sta ... <a href="/html/ALL/s/S/Separating_Words_Problem.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/S/Separating_Words_Problem.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Separating_Words_Problem" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Separating_Words_Problem" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Separating_Words_Problem" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/D/Deterministic_Finite_Automaton.html" title="Click for more on -> Deterministic Finite Automaton"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/9/94/DFA_example_multiplies_of_3.svg" title="Click for more on -> Deterministic Finite Automaton" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:DFA_example_multiplies_of_3.svg" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/D/Deterministic_Finite_Automaton.html" style="text-decoration:none;">Deterministic Finite Automaton</a></b></big></big><br> In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Hopcroft 2001: ''Deterministic'' refers to the uniqueness of the computation run. In search of the simplest models to capture finite-state machines, Warren McCulloch and Walter Pitts were among the first researchers to introduce a concept similar to finite automata in 1943. The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S0, S1, and S2 (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state ... <a href="/html/ALL/s/D/Deterministic_Finite_Automaton.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/D/Deterministic_Finite_Automaton.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Deterministic_Finite_Automaton" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Deterministic_Finite_Automaton" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Deterministic_Finite_Automaton" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/S/String_(computer_Science).html" title="Click for more on -> String (computer Science)"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/4/45/String_Variable_Diagram_Middle_Aspect_Ratio.png" title="Click for more on -> String (computer Science)" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:String_Variable_Diagram_Middle_Aspect_Ratio.png" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/S/String_(computer_Science).html" style="text-decoration:none;">String (computer Science)</a></b></big></big><br> In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathemati ... <a href="/html/ALL/s/S/String_(computer_Science).html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/S/String_(computer_Science).html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/String_(computer_Science)" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=String_(computer_Science)" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=String_(computer_Science)" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/T/Theoretical_Computer_Science.html" title="Click for more on -> Theoretical Computer Science"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/9/9d/DFAexample.svg" title="Click for more on -> Theoretical Computer Science" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:DFAexample.svg" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/T/Theoretical_Computer_Science.html" style="text-decoration:none;">Theoretical Computer Science</a></b></big></big><br> Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's ACM SIGACT, Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of n ... <a href="/html/ALL/s/T/Theoretical_Computer_Science.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/T/Theoretical_Computer_Science.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Theoretical_Computer_Science" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Theoretical_Computer_Science" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Theoretical_Computer_Science" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/O/Open_Problem.html" title="Click for more on -> Open Problem"> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/O/Open_Problem.html" style="text-decoration:none;">Open Problem</a></b></big></big><br> In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is known). In the history of science, some of these supposed open problems were "solved" by means of showing that they were not well-defined. In mathematics, many open problems are concerned with the question of whether a certain definition is or is not consistent. Two notable examples in mathematics that have been solved and ''closed'' by researchers in the late twentieth century are Fermat's Last Theorem and the four-color theorem.K. Appel and W. Haken (1977), "Every planar map is four colorable. Part I. Discharging", ''Illinois J. Math'' 21: 429–490. K. Appel, W. Haken, and J. Koch (1977), "Every planar map is four colorable. Part II. Reducibility", ''Illinois J. Math'' 21: 491–567. An important open mathematics problem solve ... <a href="/html/ALL/s/O/Open_Problem.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/O/Open_Problem.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Open_Problem" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Open_Problem" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Open_Problem" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/S/String_Operations.html" title="Click for more on -> String Operations"> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/S/String_Operations.html" style="text-decoration:none;">String Operations</a></b></big></big><br> In computer science, in the area of formal language theory, frequent use is made of a variety of string functions; however, the notation used is different from that used for computer programming, and some commonly used functions in the theoretical realm are rarely used when programming. This article defines some of these basic terms. Strings and languages A string is a finite sequence of characters. The empty string is denoted by \varepsilon. The concatenation of two string s and t is denoted by s \cdot t, or shorter by s t. Concatenating with the empty string makes no difference: s \cdot \varepsilon = s = \varepsilon \cdot s. Concatenation of strings is associative: s \cdot (t \cdot u) = (s \cdot t) \cdot u. For example, (\langle b \rangle \cdot \langle l \rangle) \cdot (\varepsilon \cdot \langle ah \rangle) = \langle bl \rangle \cdot \langle ah \rangle = \langle blah \rangle. A language is a finite or infinite set of strings. Besides the usual set operations like union, inters ... <a href="/html/ALL/s/S/String_Operations.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/S/String_Operations.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/String_Operations" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=String_Operations" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=String_Operations" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/P/Prime_Number.html" title="Click for more on -> Prime Number"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/f/f0/Primes-vs-composites.svg" title="Click for more on -> Prime Number" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:Primes-vs-composites.svg" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/P/Prime_Number.html" style="text-decoration:none;">Prime Number</a></b></big></big><br> A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which alw ... <a href="/html/ALL/s/P/Prime_Number.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/P/Prime_Number.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Prime_Number" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Prime_Number" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Prime_Number" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/M/Modular_Arithmetic.html" title="Click for more on -> Modular Arithmetic"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/a/a4/Clock_group.svg" title="Click for more on -> Modular Arithmetic" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:Clock_group.svg" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/M/Modular_Arithmetic.html" style="text-decoration:none;">Modular Arithmetic</a></b></big></big><br> In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in , but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic ''modulo'' 12. In terms of the definition below, 15 is ''congruent'' to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock. Congruence Given an integer , called a modulus, two integers and are said to be congruent modulo , if is a divisor of their difference (that is, if there is an integer such that ). Congruence modu ... <a href="/html/ALL/s/M/Modular_Arithmetic.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/M/Modular_Arithmetic.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Modular_Arithmetic" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Modular_Arithmetic" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Modular_Arithmetic" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/J/Jeffrey_Shallit.html" title="Click for more on -> Jeffrey Shallit"> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/J/Jeffrey_Shallit.html" style="text-decoration:none;">Jeffrey Shallit</a></b></big></big><br> Jeffrey Outlaw Shallit (born October 17, 1957) is a computer scientist, number theorist, and a noted critic of intelligent design. He is married to Anna Lubiw, also a computer scientist. Early life and education Shallit was born in Philadelphia, Pennsylvania in 1957. His father was Joseph Shallit, a journalist and author, and a son of Jewish immigrants from Vitebsk, Russia (now in Belarus). His mother was Louise Lee Outlaw Shallit, a writer. He has one brother, Jonathan Shallit, a music professor. He earned a Bachelor's degree in mathematics from Princeton University in June 1979. He received a Ph.D., also in mathematics, from the University of California, Berkeley in June 1983. His doctoral thesis was entitled ''Metric Theory of Pierce Expansions'' and his advisor was Manuel Blum. Advocacy Since 1996, Shallit has held the position of Vice-President of Electronic Frontier Canada. In 1997, he gained attention for the publication on the Internet of ''Holocaust Revi ... <a href="/html/ALL/s/J/Jeffrey_Shallit.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/J/Jeffrey_Shallit.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Jeffrey_Shallit" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Jeffrey_Shallit" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Jeffrey_Shallit" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/H/Hamming_Weight.html" title="Click for more on -> Hamming Weight"> <span><br><div><script src="/js/AdvertListPict.js"></script></div><br></span> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/H/Hamming_Weight.html" style="text-decoration:none;">Hamming Weight</a></b></big></big><br> The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary representation of a given number and the ''ℓ''₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James W. L. Glaisher to give a formula for the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalent to Hamming weight in the binary case, in 1954. Hamming weight is used in several disciplines including information theory, coding theo ... <a href="/html/ALL/s/H/Hamming_Weight.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/H/Hamming_Weight.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Hamming_Weight" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Hamming_Weight" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Hamming_Weight" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/A/Almost_All.html" title="Click for more on -> Almost All"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/4/49/CantorEscalier.svg" title="Click for more on -> Almost All" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:CantorEscalier.svg" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/A/Almost_All.html" style="text-decoration:none;">Almost All</a></b></big></big><br> In mathematics, the term "almost all" means "all but a negligible amount". More precisely, if X is a set, "almost all elements of X" means "all elements of X but those in a negligible subset of X". The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite, countable, or null. In contrast, "almost no" means "a negligible amount"; that is, "almost no elements of X" means "a negligible amount of elements of X". Meanings in different areas of mathematics Prevalent meaning Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) but finitely many". This use occurs in philosophy as well. Similarly, "almost all" can mean "all (elements of an uncountable set) but countably many". Examples: * Almost all positive integers are greater than 1012. * Almost all prime numbers are odd (2 is the only exception). * Almost all polyhedra are irregular (as there are only nine exceptions: the five platonic sol ... <a href="/html/ALL/s/A/Almost_All.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/A/Almost_All.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Almost_All" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Almost_All" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Almost_All" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/H/Hamming_Distance.html" title="Click for more on -> Hamming Distance"> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/H/Hamming_Distance.html" style="text-decoration:none;">Hamming Distance</a></b></big></big><br> In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of ''substitutions'' required to change one string into the other, or the minimum number of ''errors'' that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming. A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over a finite field. Definition The Hamming distance between two equal-length strings of symbols is the number of positions at which the corresponding symbols are different. Examples The symbols may be letters, bits, or decimal digits, among other possibilities. For example, the Hamming distance betwe ... <a href="/html/ALL/s/H/Hamming_Distance.html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/H/Hamming_Distance.html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Hamming_Distance" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Hamming_Distance" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Hamming_Distance" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> <tr; > <td width="15%"><p> <a href="/html/ALL/s/P/Parity_(mathematics).html" title="Click for more on -> Parity (mathematics)"> <center><img src="https://upload.wikimedia.org/wikipedia/commons/e/e1/Parity_of_5_and_6_Cuisenaire_rods.png" title="Click for more on -> Parity (mathematics)" width="100%;" height="auto;"><center></a> <a href = "https://commons.wikimedia.org/wiki/File:Parity_of_5_and_6_Cuisenaire_rods.png" target=_blank style="text-decoration:none; color:#d0d0d0;">picture info</a> </p> </td> <td valign="top"; width="75%"; > <div style="margin-left:0%; margin-right:9%";>  <div style="margin-left:2%";> <big><big><b><a href="/html/ALL/s/P/Parity_(mathematics).html" style="text-decoration:none;">Parity (mathematics)</a></b></big></big><br> In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; other ... <a href="/html/ALL/s/P/Parity_(mathematics).html" style="text-decoration:none;"> <br>[...More Info...] &nbsp &nbsp &nbsp <a href="/html/ALL/l/P/Parity_(mathematics).html" style="text-decoration:none;"> [...Related Items...] &nbsp &nbsp <a href="https://en.wikipedia.org/wiki/Parity_(mathematics)" target=_blank style="text-decoration:none;"><b> OR:</b> &nbsp &nbsp [Wikipedia] &nbsp </a> <a href="https://www.google.com/search?q=Parity_(mathematics)" target=_blank style="text-decoration:none;"> [Google] &nbsp </a>    <a href="https://www.baidu.com/s?wd=Parity_(mathematics)" target=_blank style="text-decoration:none;"> [Baidu] &nbsp </a>  </div> <br></a></a> <br> </div> </td> </tr> </table> </div> <div id="AdvertBottom1"> </div> <center> <script src="/js/AdvertBottom1.js"> </script> </center> <footer> <big><big> <div> <br><br> <br><br> <center> <br><a target="_top" href="../index.html"> HOME </a><br> <br>Content is Copyleft<br>Website design, code, and AI is Copyrighted (c) 2014-2017 by Stephen Payne<br><br> <a target="_top" href="https://donate.wikimedia.org/w/index.php?title=Special:LandingPage&country=US&uselang=en&utm_medium=sidebar&utm_source=donate&utm_campaign=C13_en.wikipedia.org"> Consider donating to Wikimedia </a><br> <br> As an Amazon Associate I earn from qualifying purchases <br></center> </div> </big></big> </footer> <div id="AddedByJS"> </div> <script src="/js/site.js"> </script> </body>