Regular Expressions - a Graphical User Interface

Transcription

1 Regula Expeion - a Gaphical Ue Inteface Stefan Kah Univeity of Kent at Cantebuy Computing Laboatoy mk@ukc.ac.uk Septembe 13, 1999 Abtact Regula expeion ae a tandad tool fo language deciption, in ue fo canne geneato and vaiou each engine. Theefoe, they and thei connection to finite automata i an ubiquitou pat of any compute cience yllabu. Thi pape i about a gaphical ue inteface that demontate the tanlation of egula expeion into nondeteminitic finite automata. We dicu the deign choice of thi tool and elate it to othe tanlation technique. 1 Intoduction Regula expeion ae o widely ued that they baely need an intoduction. In CS teaching, they ae taditionally aociated with coue on compile contuction lagely becaue fomal language theoy ha become a bit too unfahionable on it own. Similaly, textbook on the ubject alway include a ection on egula expeion and egula language, and explain how they can be tanlated into a coeponding finite automaton. The tanlation of egula expeion ae typically decibed in a gaphical way, one tanlation ule fo each connective. One could even view thee ule a fomal gaph gamma ule, e.g. in the tyle of [HK87], which how that they follow a vey tict patten. Geneally, egula expeion ae jut about the implet pat of a Compile coue. Thee hould not be any need to loe even the weaket tudent on that ubject, o to pend moe than a tiny amount of time explaining them in lectue. Epecially, the gaphical fom of the tanlation ule hould help. Howeve, it i not quite a imple a that in pactice. The ule in the liteatue deal with the geneal cae, they make wot-cae aumption of what could happen elewhee, and conequently they ceate unneceaily lage numbe of tate and even moe unneceaily lage numbe of -tanition. A a eult, thi i unneceaily confuing, even moe o ince ituation that equie all 1

2 thi ovehead do not aie vey often. Apat fom the confuion, a mall NFA make a ubequent tanlation into a DFA le daunting. In examination on thi ubject, when we ak tudent to tanlate a egula expeion into a finite automaton, we can obeve two kind of pefect anwe: tudent who have lavihly memoied the ule and include evey illy -tanition the tanlation demand tudent who have undetood the concept of NFA and daw the NFA by hand and intuition Amongt the impefect anwe we often find vaiation of the actual ule, except that tudent often eithe foget the odd -tanition o daw a few too many. In hot, it would be nice to pefom a moe ophiticated tanlation that ave tate and tanition and look le myteiou when applied to concete example becaue all geneated -tanition have a pupoe. On the othe hand, we nomally would not want to dwell on thee ophitication in lectue (o even textbook). I implemented a gaphical ue inteface that applied uch lightly moe ophiticated tanfomation ule which keep the et of tate and tanition mall. The implementation i a Java applet (made Java 1.1 compliant to inceae bowe compatibility) located at The ue type in a egula expeion which i then tanfomed tep by tep into the coeponding NFA; each tanfomation tep i invoked by a button pe. The idea i fo tudent to play with thi tool in thei own time to get an intuitive undetanding about egula expeion and NFA. An impotant motivation of the applet wa to avoid the ceation of NFA with too many unneceay tate and unneceay -tanition. Thi i diffeent fom the jflap tool [GR99] which uppot (ince veion 3.1, Augut 1999) a tanlation of egula expeion into NFA a well, but which tick to a much imple tanlation cheme. 2 Stategie of tanlation Although the flavou of the tanlation ule i alway the ame, thee i a conideable vaiation in the liteatue about which ule to ue. Thee i alo the quetion of the geneal tategy of the ule. The two main tategie ae: top-down; thi tategy tat with an edge labelled with a egula expeion and then applie the ule tep by tep until no futhe efinement ae poible bottom-up; hee, fit the atomic component of the egula expeion ae tanlated into NFA the ule ay how thee NFA ae then combined. 2

3 The mot commonly ued fom in the liteatue i bottom-up [ASU86, TS85, Ma91, Pa92], but top-down ha ome uppote a well [WM95, PP92]. Fo hand-dawing pupoe, the bottom-up tategy i bet, fo two eaon: fit, it doe not equie the eaue of ealie dawn bit; econd, the gaph gow outwad which mean that one uually avoid ovecowding poblem in the middle of the dawing aea. Fo a gaphical ue inteface the choice between thee two tategie hould be the othe way aound. The eaon fo thi i that a bottom-up tategy wok (at leat conceptually) with egula expeion which have finite automata a thei component, while top-down imply equie egula expeion a label of edge. The fome i a conideable challenge 1 when we finally face the quetion: how do we daw it? The latte i not. Still, the diffeence between both tategie i lagely upeficial, a it i uually eay to deive a top-down veion fom bottom-up ule and vice vea. Thee ae othe poible vaiation one can employ: Appel ue in [App98] a diffeent (alo bottom-up) tanlation cheme that doe not tanlate into NFA, but into omething one could call NFA with a half-looe initial edge. One can ceate an NFA fom the final eult of hi tanlation by connecting the looe end of the half-looe edge to a feh initial tate. The advantage of hi cheme ove the one in [ASU86] i that it need fewe tate the ub-automata can often be linked with the looe edge diectly, intead of having intemediate tate and mediating -tanition. Bentein ecently invented an allegedly new tanlation tategy fo egula expeion [Be99] which alo keep the numbe of tate elatively mall (oughly equal to the ize of connective). Thi tategy appea to be completely diffeent a it ue egula expeion a tate. The geat appeal of thi tategy i that the language of a egexp-tate i exactly the language of the NFA wee thi tate the ole accepting tate. Fo gaph-dawing pupoe, Bentein tanlation ha the big diadvantage not to be fully compoitional. With thi, I mean that a efinement tep could be foced to daw a new edge between two tate which ae located in completely diffeent pat of the gaph. Howeve, it i poible to view hi ule a edge-eplacement ule; the non-compoitionality can be olved fo the pice of (poibly) geneating a few moe tate, without affecting hi geneic claim about the numbe of geneated tate. Appel ule, when tanlated into the wold of edge-eplacement, ae upiingly imila to Bentein, the only diffeence being a lightly moe expenive ule fo the choice opeato. 1 Notwithtanding, JFLAP 3.1 ue thi tategy with le than pefect eult. 3

4 3 The Rule Fo ou pupoe we tick to the peentation of ule a edge-eplacement ule, i.e. we follow a top-down appoach. Set of tanfomation ule uually wok with ome kind of invaiant that i maintained thoughout, typically fo coectne pupoe and to contain tategowth. One invaiant almot 2 evey tanlation ytem ue i to etict itelf to a ingle accepting tate and we will do the ame. So, in the following the tem NFA will implicitly cay thi etiction. The othe ued invaiant ae afety citeia fo the initial and accepting tate. An NFA i called in-afe if it initial tate ha no incoming tanition, and dually it i called out-afe if it accepting tate ha no outgoing tanition. It i afe if it i both in-afe and out-afe. Notice that we can eaily make an NFA in-afe by adding a new initial tate that i pepended with an -tanition to the old one. An analogou agument applie fo out-afety. Many of the tanlation cheme wok by maintaining afety a an invaiant, i.e. thei ule alway poduce a afe NFA, and the fact that they do can be exploited fo the connective. Thi applie fo example to the tanfomation ule in [WM95, ASU86, TS85]. One can fine-tune the tanlation poce a little by woking with a weake invaiant. Appel [App98], Bentein [Be99], Matin [Ma91], and JFLAP [GR99] all ue cheme that only guaantee in-afety. 3.1 Sequencing Conide fo example the vey imple tanfomation ule below fo teating equential compoition of egula expeion. x y x z y What could be imple and moe obviou than thi ule? Howeve, even thi imple ule involve aumption about afety: It i coect if the eplacement of i out-afe o the eplacement of i in-afe. It i in-afe if i, and out-afe i i. Thee ae faily weak equiement and theefoe mot tanlation cheme ue thi ule. In paticula, any tanlation cheme that ha othewie eithe in-afety o out-afety (o both) a an invaiant can ue thi ule, becaue it i not only coect but maintain the invaiant. Thee i a afe ule though, ued e.g. in [PP92, Lou97, HU79]: x y x a b y Thi till inheit the in-afety fom and the out-afety fom, but it doe not equie eithe afety of o fo it own coectne. Bottom-up tanlation cheme that pemit multiple accepting tate (e.g. [GR99, Ma91]) 2 The only exception I know ae [Ma91, GR99]. 4

5 alo ue thi ule to avoid copying egula expeion they would othewie need one copy of fo evey accepting tate of. Temblay & Soenon go upe-afe 3 by futhe adding epilon-tanition at beginning and end. If we want to contain tate-gowth we clealy would like to apply the fit ule wheeve poible. If we employed a tanlation cheme that peeved afety (o jut in-afety) then we could ue that ule in evey cae. The applet doe not maintain afety, not even in the weake fom of in-afety o out-afety. What it doe intead i to label edge with afety equiement. In a lightly implified fom thi goe a follow: x y x z y The afety equiement that i in-afe i expeed hee by double-lined connection. Thi alo mean, of coue, that the aow we tated with could have had it own afety equiement. We have to deal with that, e.g. by poviding an additional ule: x y x z y Thee i a dual inheitance of an out-afety equiement (o fa we do not have any but they how up late) which goe to the econd edge. Howeve, thi i not 100% ideal. Fo ou initial ule we had the choice impoing eithe in-afety fo o out-afety fo. If we ae unlucky in ou choice then we ceate one tate and one -tanition too many, i.e. if the afety citeion we choe to impoe i violated while the one we did not imply hold. The implementation addee that by uing the afe ule wheneve and ae likely to clah, i.e. when end with an iteation and begin with one. 3.2 Choice Fo the eplacement of a choice edge x y thee ae quite a few diffeent poibilitie available. The Dagon book play it vey afe by tanlating into: a x c b y d Thi i vey afe a it i coect and afe without any afety equiement fo and. Thi i the mot commonly ued ule in the liteatue [ASU86, TS85, PP92, Lou97, Pa92, Mo98, HU79]. 3 Quite fankly, thi i mad. Unupiingly, they optimie quite a few away when they demontate the tanlation at an example. 5

6 The pice paid fo thi amount of afety ae fou exta tate and fou exta - tanition. Bentein and Sippu & Soialon-Soininen tanlate two of thee into afety equet (which in both cae ae invaiant of thei epective tanlation cheme): a x y b a x b y The ule fom [SSS88] (on the ight) impoe both in-afety and out-afety. The out-afety equet i indicated gaphically by the cloed aow-head. Bentein ule (on the left) popagate and demand in-afety. Appel, Matin and JFLAP ue light vaiation of thi ule: Appel [App98] make it inafe by pepending an -tanition at the beginning; Matin and JFLAP [Ma91] ave the out-going -tanition and imply pemit many accepting tate. In fact, we can eliminate all exta tate and -tanition fo the pice of afety equet. Thi i paticulaly ueful if the tanlation cheme popagate full afety anyway. x y Wilhelm & Maue tanlation cheme ceate afe NFA, and o they can (and do) ue thi ule. My applet ue thi ule a well; ince it doe not alway geneate afe NFA it ceate intead the coeponding afety equet, i.e. full afety fo both and. Mot bottom-up cheme do not ue thi ule even if they ceate afe NFA, fo the imple pagmatic eaon that a bottom-up tategy face the awkwad cenaio (fo hand-dawing pupoe) that the initial and accepting tate of two automata need to be identified. 3.3 Iteation Thi i pehap the tickiet 4 of all the cae, tanlating x y. Mot book go hee fo the vey afe veion: x a b y 4 An ealy veion of Appel book even ued an unound tanlation. 6

7 Thi i coect and afe without any afety equiement fo. Seppu & Soialon-Soininen vay thi ule lightly by having an -tanition fom a to y intead of x to y thi i only ound if i in-afe. Bentein ha a niftie tanlation cheme (alo ued by Appel and Matin). All hi tate ae egula expeion and we can each one of thee tate fom the initial tate with a wod w only if w i in the language 5 of. Theefoe, y mut be equal to x, and all we need i an additional tate x with the athe obviou tanition between thoe tate deived fom the univeal popetie of. Long toy, hot tanfomation ule: x y z Hee, the feh tate z tand fo the language x. A a geneal ule (outide the context of Bentein tanlation cheme) thi i coect if i in-afe, and it i itelf in-afe (and not out-afe). JFLAP ue a lightly weid vaiation of the ule in which not y i the accepting tate but x and z ae. The above i a imple ule fo the popagation of in-afety; thee i a dual one which poduce an out-afe NFA: x z y One can do lightly bette than thee ule by tuning one of the tanition into a afety equiement. Hee i uch a ule which alo geneate in-afety: x y I did not choe ule of that kind fo the gaphical ue inteface, becaue thee little elf-loop ae athe cumbeome fo dawing pupoe. In which diection hould they go, what hould be the adiu of the loop, how do we cay on if i futhe efined? If thee choice ae made badly then the layout i quickly uined. Fo implicity (fewe cae ditinction and imple gaph layout) I did not ue Bentein ule eithe, intead I went fo the following: x y 5 In ou etting the wod could contain itelf egula expeion in which cae the condition i that the language of w i a ub-language of. 7

8 ( ) = = (p q) = ( q) if p = (pq) = (p q) if p and q ae nullable p = p p q = p + q if q i nullable p q = p + q p = p if p i nullable Table 1: Optimiation Thi ule i coect with the indicated (full) afety equiement fo. If thee wee no afety equiement fo the edge we tated with thi ule i pefeable to Bentein anyway a it ceate fewe tate. Othewie, Bentein ule i lightly bette a it geneate one afety equiement fewe. Inteetingly, an appaently imila ule fo + can dop it afety equiement entiely: x y Baed on thi, it i clea that the ulta-afe ule fo, mentioned at the beginning of thi ection, can be een a eulting fom the equality = ( + ). 3.4 Atomic Regula Expeion The atomic egula expeion, i.e. chaacte,, and alway poduce afe connection. The only efinement ule i the emoval of any -labelled edge. Apat fom that, afety containt ae emoved. x c y x c y Tanlation cheme which ae not baed on edge-eplacement [Ma91, App98] can do lightly bette with -egexp a they coepond to ingle-tate NFA. 3.5 Optimiation The applet alo employ (optionally) a numbe of optimiation and implification, epecially in connection with the iteation opeato. The mot ignificant one ae lited in table 1. 8

9 Thee equation can be een a conditional tem ewite ule, going fom left to ight, a thi i the diection in which we ave tate and tanition (o even weaken afety equet only). Thi i not neceaily the cae concening the ule p q = p + q which i theefoe only applied fo cetain p. Example: the nomal fom of (a (b c) ) and (p h) b ae (a b c) and (p h) + b +, epectively. The ue of the applet can witch the optimiation on and off, even in the middle of the tanfomation poce. The eaon fo giving that flexibility i that on the one hand the combined effect of the optimiation can be athe puzzling fo the uninitiated, on the othe thei complete abence would too eaily ceate ovecowding poblem in the dawing aea. 3.6 Counting State Since mot et of tanlation ule wok in a athe context-fee manne, it i faily eay to compute the numbe of tate they geneate. Thi numbe can nomally be expeed a a m + b n + c p + 2, whee m, n, and p ae the numbe of choice opeato, iteation opeato, and equencing opeato in the oiginal egula expeion, and a, b and c ae contant that depend on the tanlation cheme. The eaon fo the +2 i the initial cenaio of the top-down tanlation which ha aleady one initial and one accepting tate. Hee i a table giving thee contant fo ome of thee cheme: The table i Souce choice ite eq cha plu example [TS85, Mo98] [HU79, PP92, Lou97] [ASU86, Pa92] [Ma91, GR99] [SSS88] [App98] [Be99] [WM95] thi Table 2: Computing the tate numbe to be ead a follow: if the oiginal egula expeion ha m (binay) choice, n iteation, p (binay) equence and q ingle-chaacte egula expeion then, ay, the tanlation cheme in [ASU86] poduce an NFA with 4m + 2n + p + 2 tate. The column on the ight how thi numbe fo the ample egula expeion (b a x)y z m. The eaon the table ha 5 cental column (athe than 3) i that not evey cheme can be een a an edge-eplacement ytem, ome ae intinically bottom-up. Thi applie in paticula to [Ma91] and [GR99] fo which the numbe of tate of the geneated NFA i m + n + 2q, whee q i the numbe of ingle-chaacte egula expeion. Alo, Appel NFA-mutant ae jut a wee bit diffeent. 9

10 The ange 0 1 and 0 2 in two of the entie indicate it depend on the context. Fo the applet, thi numbe depend on the inheited afety equiement. Moeove, the entie fo the applet (and alo Bentein tanlation) do not take the optimiation into account, e.g. a equence opeato inide an iteation may be optimied away by the applet, and Bentein tanlation implicitly exploit law uch a ( t) = ( t). 4 Implementation Detail Ente a egexp: (b a*x)y (z*m*) Tanfom Optimiation Unpaing give: (b a* x) y z* m* b S 1 % % 5 a % 6 x 0 z % y 2 % 3 m % 4 % E Figue 1: Pogam appeaance The pictue how the geneal appeaance of the applet afte a few tep. One egula expeion (hee: (b a x)y z m ) ha been typed in and completely tanfomed in eveal tep. 10

11 egexp equence egexp egexp equence equence iteation equence equence iteation iteation pimay iteation iteation * iteation iteation + pimay % pimay (egexp) pimay chaacte Table 3: Input Gamma 4.1 The Ue Inteface The applet ha fou component: thee panel, and a canva. The fit (oange) panel ak fom the eade to input a egula expeion. The text of the input field of thi panel i paed to a yntax analye (a hand-witten LL(1) pae). The econd (magenta) panel then diplay eithe an unpaed veion of the input (which could have fewe paenthee) in it textfield, o an eo meage if the input wa yntactically incoect. The thid panel contain the tanfom button and the optimie check-box. Table 3 decibe the ecognied yntax fo egula expeion. The teminal chaacte tand fo any alpha-numeical chaacte. The % epeent, epeent. Space and tab ae allowed in the input but ignoed. The canva i the dawing aea of the applet. It ize can be vaied by modifying the applet dimenion in the accompanying HTML file. Initially the canva diplay two tate, S and E, the initial and accepting tate of the NFA, plu an unmaked edge going fom S to E. When a egula expeion ha been uccefully paed it become the label of thi edge. By clicking the tanfom button an edge-eplacement ule i invoked and the gaph change accodingly. The edexe ae choen in a beadth-fit manne. A afety equiement of both in-afety and out-afety i indicated by diplaying the aow in blue intead of black. Slightly diffeent hade of blue ae ued to indicate in-afety o out-afety only. Thee weake equet ae only geneated when the optimiation i witched off to cove fo the cae that the optimiation i witched on duing the tanlation poce. 4.2 Optimiation If the optimiation check-box i witched on, the egula expeion ae fit optimied befoe the tanfomation poce can poceed. Thi optimiation eplace egula expeion by nomal fom w..t. the ewite ule mentioned ealie, plu a few othe uch a = =, etc. 11

12 If the optimiation i witched off then ome edge labelled with choiceegexp have pecific (context-dependent) afety citeia impoed on them. Thee i a ubtle eaon why thi i neceay hee and not in the peence of optimiation ule: the edge-eplacement ule fo choice will alway poduce a afe NFA, theefoe any afety impoed on a choice-edge appea to be edundant. Howeve, the ue i allowed to witch optimiation on in the middle of the tanfomation poce, in which cae all cuent egexp-label ae optimied. In thi ituation a choice-egexp can be eplaced by a egula expeion of a diffeent kind and in thi ituation the impoed afety citeia do matte. If, on the othe hand, uch edge with choice-egexp label ae ceated when optimiation i witched on then the above ituation cannot aie: thee edge ae aleady labelled with nomal fom and choice nomal fom ae intinically afe. 4.3 Gaph Layout The gaph layout i modeately afely computed it i poible fo node and edge to be placed at vey awkwad place, cauing ovecowding, but thee i a check that enue that the canva aea i neve left. New node ae only eve ceated by plitting a (poibly cuved) edge into egment, e.g. if we efine an edge labelled abc then we need two intemediate node, the cente of which ae placed at equal ditance along the oiginal edge. An edge labelled with e.g. abc o a b c i efined in a ingle tep, giving equal oom fo all it component. It imply look nice to give each of a, b, and c a thid of the available pace each intead of giving a half, and b and c ubequently a quate each. It alo make ovecowding le likely. All cuved line ae dawn uing Java dawac method, moe pecifically they ae all egment of a cicle 6. Java 1.1 povide little uppot fo dealing with cicle egment, in paticula affine tanfomation ae lacking (uppoted in Java 1.2 but not hee). They wee e-implemented and ued quite extenively, e.g. fo equipping edge with aow-head. Initially thee wee ome poblem with pinting the pictue, i.e. wong cicle egment wee dawn and exta line appeaed on the pint-out. The latte wa a known Java-bug (numbe 4,076,291), the fome a (then) unknown one. The check that the dawing tay on the canva wok a follow. The only ik to leave the canva i fom dawing cuved aow fo altenative and iteation, becaue all newly geneated node lie on peviouly geneated line 7. The check fo new ac fit compute all inteection of the cicle with the canva bode and then tet whethe any of thee point i on the ac. Since we want to be able to daw node along uch line (which have ome pace 6 The dawac method uppot the dawing of ellipe-egment, but unfotunately thee ellipe cannot be tuned, i.e. the line though the two focal point of the ellipe i alway paallel with eithe x-axi o y-axi. 7 Thi i one of the majo eaon fo chooing the ealie decibed tanlation cheme fo and +. 12

13 q f c p t Figue 2: Canva Check demand of thei own) all canva bode ae educed by the (fixed) adiu of node. Computing the inteection of a cicle with the bounding aea of the canva i faily imple, epecially a the bode line ae paallel with eithe x-axi o y-axi. Fo example, the cicle (x c x ) 2 +(y c y ) 2 = 2 (with cente C = (c x, c y ) and adiu ) inteect the vetical line x = a if and only if 2 (a c x ) 2 i poitive in which the cae the two inteection ae (a, c y ± 2 (a c x ) 2 ). To check that uch a point P i on the ac, we compute the angle between x-axi and the line CP. An example can be een in figue 2: we want to daw the (bold) ac fom f to t. The cicle thi ac belong to ha two inteection with the canva aea (the ectangle), point p and q. Since neithe the line cp no the line cq i in the ac egment of the cicle it i clea that thi dawing tay on the canva aea and i theefoe pemitted. 5 Summay The implemented applet i a nice little toy fo tudent to get to gip with egula expeion and finite automata. Becaue it make a lot of ue of context infomation it can opeate with moe ophiticated tanlation cheme than the one in the liteatue. In paticula, it poduce fewe tate and fewe tanition. Thi ha two advantage: fit, the tudent ee a bit of elation algeba in action, and econd, all thee mytifying uele -tanition which the known tanlation cheme o happily geneate ae omitted by the applet. If thee i 13

14 an -tanition then thee i a good eaon why it i thee. Thee i till oom fo impovement though, e.g. it i poible to educe the numbe of tate even futhe (epecially by uppoting tanition fom a tate to itelf), and one could implement futhe optimiation, uch a ( t) = ( t). Alo, the placement of new edge and node on the dawing uface could be made intelligent, i.e. awae of the cuent tate of the dawing, to avoid node being placed on top each of othe o edge coing node. Refeence [App98] Andew W. Appel. Moden Compile Implementation in Java. Cambidge Univeity Pe, [ASU86] Alfed Aho, Ravi Sethi, and Jeffey Ullman. Compile Pinciple, Technique, and Tool. Addion-Weley, [Be99] [GR99] [HK87] [HU79] Daniel J. Bentein. A univeal patten-matching automaton. Univeity of Illinoi at Chicago, Depatment of Mathematic, Statitic and Compute Science, Eic Gamond and Suan H. Rodge. Uing JFLAP to inteact with theoem in automata theoy. In 30th SIGCSE Technical Sympoium on Compute Science Education, page ACM, Anneget Habel and Han-Jög Keowki. Chaacteitic of gaph language geneated by edge eplacement. Theoetical Compute Science, 51:81 115, John E. Hopcoft and Jeffey D. Ullman. Intoduction to Automata Theoy, Language and Computation. Addion-Weley, [Lou97] Kenneth C. Louden. Compile Contuction. PWS Publihing Company, [Ma91] John C. Matin. Intoduction to Language and the Theoy of Computation. McGaw-Hill, [Mo98] Benad M. Moet. The Theoy of Computation. Addion-Weley, [Pa92] [PP92] Thoma W. Paon. Intoduction to Compile Contuction. Compute Science Pe, Thoma Pittman and Jame Pete. The At of Compile Deign. Pentice Hall, [SSS88] Seppo Sippu and Elja Soialon-Soininen. Paing Theoy, volume 1. Spinge,

15 [TS85] Jean-Paul Temblay and Paul G. Soenon. The Theoy and Pactice of Compile Witing. McGaw-Hill, [WM95] Reinhad Wilhelm and Diete Maue. Compile Deign. Addion- Weley,