A New Technique for Reachability of States in Concatenation Automata

We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the concatenation of two languages, and thus in establishing the state complexity of concatenation as an operation. Typically, ad-hoc induction arguments are used to show particular states are reachable in concatenation automata. We prove some results that seem to capture the essence of many of these induction arguments. Using these results, reachability proofs in concatenation automata can often be done more simply and without using induction directly.Comment: 23 pages, 1 table. Added missing affiliation/funding informatio

Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages

A language $L$ over an alphabet $\Sigma$ is suffix-convex if, for any words $x,y,z\in\Sigma^*$, whenever $z$ and $xyz$ are in $L$, then so is $yz$. Suffix-convex languages include three special cases: left-ideal, suffix-closed, and suffix-free languages. We examine complexity properties of these three special classes of suffix-convex regular languages. In particular, we study the quotient/state complexity of boolean operations, product (concatenation), star, and reversal on these languages, as well as the size of their syntactic semigroups, and the quotient complexity of their atoms.Comment: 20 pages, 11 figures, 1 table. arXiv admin note: text overlap with arXiv:1605.0669

Status of twist-2 operator dimensions at O(1/N_f)

We review the computation of the anomalous dimensions of the twist-2 unpolarized operators in the large N_f expansion. Results are discussed for the predominantly gluonic singlet operator and the O(1/N_f) part of the 3-loop splitting function is given.Comment: 4 latex pages, contribution to DIS 9

Opera Man and the Meeting of ‘Tastes’

The introduction of the Super League in 1996 heralded a more commercial era for professional rugby league in the United Kingdom (Meier, 2000). Part of the associated package has been an entertainments programme around games. Initially hesitant following a near disastrous first Super League season, Leeds Rhinos (the brand name adopted by Leeds Rugby League Football Club) have embraced this initiative. An MC introduces a bill that variously includes: the team’s mascot, Ronnie the Rhino; a dance team and community dance groups; children’s mini rugby; local singers and tribute acts; silly games featuring people from the crowd; presentations of former stars and special appearances (e.g. the Forces). While very deliberately identifying the persistence of some rationalist/modernist dimensions of Super League rugby Denham (2000: p. 289) observes of this development: Part of the attraction is to sell more than the game by adding entertainment and additional spectacle through cheerleaders, mascots and fireworks. Postmodernism has been seen as reflecting the fragmentation and diversification of culture and, along with it, the breakdown of older categories and binary divisions that have been associated with modern culture, such as high/low... One of the most successful elements of the wider entertainment package at Leeds’ games has been ‘Opera Man’. This is the nickname given to John Innes, the classically-trained singer, by the crowd at Headingley Stadium (the home of the Rhinos). Some seem unsurprised by the success of this initiative, but it piqued my curiosity as an unlikely coming-together of two leisure interests. As a fan my initial reaction was similar to what one of my respondents described: “When he first came in you could see in the crowd it was ‘You what? An opera guy coming to sing at rugby league?’. And then he became a cult figure … Who would have thought that rugby league would have been the home for Opera Man?” (Chrissy). On one of the blog sites Jerry Chicken commented: “Opera Man” as he has become known to your average rugby league fan who, it has to be said, would in all other circumstances call John Innes and his ilk “big puffs” has introduced the concept of the aria to the sport so much so that the crowd actually sing along with him now, even though they know not the words and simply make the sounds. http://jerrychicken.blogspot.co.uk/2007/10/opera-man.html [last accessed 27th January 2013] To explore what underlies the apparent success of this Heston Blumenthal recipei, this paper borrows concepts from Bourdieu (1984)