A palindrome is a word, phrase, number or other sequence of units that has the property of reading the same in either direction (the adjustment of punctuation and spaces between words is generally permitted). Composing literature in palindromes is an example of constrained writing. The word "palindrome" was coined from Greek roots palin (πάλιν; "back") and dromos (δρóμος; "way, direction") by English writer Ben Jonson in the 1600s. The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (καρκινική επιγραφή; crab inscription), or simply karkiniêoi (καρκινιήοι; crabs), alluding to the backward movement of crabs, like an inscription which can be read backwards. The most familiar palindromes, in English at least, are character-by-character: the written characters read the same backwards as forwards. Palindromes may consist of a single word (civic, level, racecar, Malayalam), or a phrase or sentence ("Neil, a trap! Sid is part alien!", "Was it a rat I saw?", "Mr. Owl ate my metal worm", "Sit on a potato pan, Otis", "Satan, oscillate my metallic sonatas", "Rats live on no evil star."). Spaces, punctuation and case are usually ignored. Some palindromes use words as units rather than letters. Examples are "fall leaves after leaves fall", "First Ladies rule the State and state the rule: ladies first" and "Girl, bathing on Bikini, eying boy, sees boy eying bikini on bathing girl". The command "Level, madam, level!", composed only of words that are themselves palindromes, is both a character-by-character and a word-by word palindrome. A palindromic number is a number where the digits, with decimal representation usually assumed, are the same read backwards, for example, 58285. They are studied in recreational mathematics where palindromic numbers with special properties are sought. A palindromic prime is a palindromic number that is a prime number. A palindrome in which a recorded phrase of speech sounds the same when it is played backwards was discovered by composer John Oswald in 1974 while he was working on audio tape versions of the cut-up technique using recorded readings by William S. Burroughs. Oswald discovered in repeated instances of Burroughs speaking the phrase "I got" that the recordings still sound like "I got" when played backwards. In the automata theory, a set of all palindromes in a given alphabet is a typical example of a language which is context-free, but not regular. This means that it is theoretically impossible for a computer with a finite amount of memory to reliably test for palindromes. (For practical purposes with modern computers, this limitation would only apply to incredibly long letter-sequences.)
Additionally, the set of palindromes cannot be reliably tested by a deterministic pushdown automaton, and is not LR(k) parseable. When reading a palindrome from left-to-right, It is essentially impossible to locate the "middle" until the entire word has been read. Then there's this film...
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