by Charlton D. Rose
Jurm (Java URM) is a java-based utility that simulates a Universal Register Machine (URM), as described in Computability, by N. J. Cutland. Jurm is capable of parsing and converting text-based URM program listings into URM program numbers, and vice-versa. Jurm can execute nearly any interesting URM program, given optional, arbitrary inputs and an optional step limit. Upon completion of a URM simulation, Jurm outputs an execution summary.
Because of the generality of this program, it is quite possible that Jurm contains the meaning of the universe. :-)
Jurm is a command-line utility. The command syntax is:
java urmprogram[param1[param2[...]]][timesteplimit]
program is either an integer representing the program's code number (as described in chapter 4 of Cutland's text) or the name of a text file containing the program's listing.
param1, param2, ... are input values supplied to the URM program, i.e., the initial values of the first few registers in the register bank. By default, all registers begin with an initial value of zero.
steplimit, if specified, is the maximum number of steps the URM processor should execute before "giving up" on the program. This parameter is useful for situations in which the input vector may not be in the domain of the program (i.e., the program does not halt when started with the given input).
Jurm generates an execution summary when the simulated program halts or when the step limit, if set, has been reached. The meaning of the output summary should be obvious to anyone who has studied Cutland's text. Examples are given below:
We will use Jurm to verify example 4.1.5.a of Cutland's text.
>java urm 9007203549970431 Decoding program...done. Executing program...done. Execution summary: ------------------ program: 9007203549970431 input: none output: 0 time: 3 steps Program listing: ---------------- 1: T (1, 3) [#18] 2: S (4) [#13] 3: Z (6) [#20] Program code: ------------- 9007203549970431
Note that instruction code numbers are shown next to each instruction in the program listing.
We will load and execute add.urm, the textual representation of a URM program, to determine the value of 51 + 8. A listing of add.urm is shown below:
top: J (3, 2, end) S (1) S (3) J (1, 1, top) end:
Note that the program listing shows labels in place of instruction numbers. Jurm will automatically convert these labels into instruction numbers when it parses the program text.
To run add.urm, we simply indicate the filename on the Jurm command line, along with the input parameters (which, in this case, are 51 and 8).
>java urm add.urm 51 8 Resolving labels...done. Loading program...done. Executing program...done. Execution summary: ------------------ program: add.urm input: (51, 8) output: 59 time: 33 steps Program listing: ---------------- 1: J (3, 2, 5) [#73727] 2: S (1) [#1] 3: S (3) [#9] 4: J (1, 1, 1) [#3] Program code: ------------- 76090488...69396735
(In the interest of brevity, the program code number is not shown in its entirety because it contains over 22,200 decimal digits. See Appendix B for the complete output.)
The function of program #176538093190184139370036875193483265 is defined as
We will execute this program on the input (10, 5), for no more than 100 steps.
>java urm 176538093190184139370036875193483265 10 5 time 100 Decoding program...done. Executing program...aborted. Execution summary: ------------------ program: 176538093190184139370036875193483265 input: (10, 5) output: unknown time: not less than 100 steps Program listing: ---------------- 1: S (1) [#1] 2: J (1, 2, 4) [#111] 3: J (1, 1, 1) [#3] Program code: ------------- 176538093190184139370036875193483265
The output shows that with the given input, the program did not halt in 100 steps.
While no program can ever be written to execute all URM programs on all domains, Jurm supports a very large subset of all possible programs and domains. (Unfortunately, the entire set is much larger.) Theoretically, Jurm can load and execute any program containing less than 231 instructions. (It is unlikely that anyone will soon a program larger than this.) The register bank has theoretically unlimited capacity. It supports any number of registers, and each register can hold any non-negative integer value.
In practice, however, the actual limits of Jurm are not dependent on the theoretical limits described above, but rather by the finite memory capacity of the environment in which Jurm runs, i.e., the JVM. For most interesting programs, the final stage of the URM simulation, in which the universal program code is computed, will abort with an OutOfMemoryException.
A zip file containing all of Jurm's compiled class files, including source code, can be downloaded from
jurm.zip
Admittedly, the program code number for the addition operator is not in itself very useful. However, it serves as a good example for illustrating how even the simplest programs can have extremely large program numbers.
>java urm add.urm 51 8 Resolving labels...done. Loading program...done. Executing program...done. Execution summary: ------------------ program: add.urm input: (51, 8) output: 59 time: 33 steps Program listing: ---------------- 1: J (3, 2, 5) [#73727] 2: S (1) [#1] 3: S (3) [#9] 4: J (1, 1, 1) [#3] Program code: ------------- 76090488372384620127756863083935061906946106970468276739002812075602101978733100 33403096847933263010179059207226650141692732249096625652786967176680596565195834 60995831417635937328808149067755161185727521357842126185836042501644528990322289 83159724844106177421577481176216630872547181660946644038632270092962114057226752 63019258491091806616904813338242481870546785135341710044055739554082429950220731 30345618021637953472849584112004738847447159066946060787526088793330812126857498 63359524767706003584758665088034284790618992497449261111106979363708997054318101 58940337828177689848547068726451636764608545489146106115110682800860541189745280 57715964356693632930985691804618383779981127525185815463444386455057812327825545 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38929719256774261653800992909919077298668641600897223980618978555141395888385373 25403212145076024895188540714626002306210971949398123419857909896090713969750067 71817376933126365273097543021242042022956164562022567633159635727915848366558178 24624298300956475928834115136007199215995866053437084685573083182598800194650589 43631468170700997528818612938011930919598465757866014081435157259352206611898852 08967472345328433503884098198615114629506168663704229568622452790288422636020973 37714253239202717971308873481572794095409160759881667296820681403455480791667362 53076755198071925310430908241969320754535559957594540848638196529875092017900336 73766526709866387000172448401384024486324672998064668294080073885005439215758037 80012779278971375989636779016308808861147530139039930729532677456513968634754443 86162448349119495431650469434187785867884334386468021294227004047196149164216682 40802518686208782303335730379485712972011709753814393601784399860379183609503190 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05938263595752483323157767199230390564352103348135155906259129493751649523469569 25569356084290334280723490016428217056816981994497129347743885765505577829409722 23859113609488013102140764353184920926101706287480394447705253311300139394981383 26326735197992529525147223617631412623649025333697511367027474537345192888192808 93259281607996226569443002118753062792508902657369925760130574140423084076434087 78085020598149091502525643059698170668979818053567266922251381761307483956420034 78211952300396253193265609009990253308945342491129584194854863367973536673822396 47974705688590896094449075202612780755690663399013337636743757407976497027702646 76404043590798647685161332232124002380123321902387041202418838016260971611188936 72758706556902117847814422543556463829559893577342533103122053127458617760062078 61866954575791071967671835970556078289786152355731450000919168980474419640625313 50722149247853193577339632999954487279663736916497304477067329906385224294650238 21029835390061191077773726692524416144172071006011324918869712549334320422844012 85872577493302915826165723204203906011046930051053623921560773606819125411663232 90151936650113935303507537896693891204870633487180644725175160956048452649301156 62517929491371504022313168875707602367581191003203511232778586834638386976384674 03901772601202964119616868855584354258750481078698504954843629811915773056014718 47033706500813941537296933240026711616181864153428248219963434378309809078922662 25006116520253248534705858063036487698593759135886654332542332772393984859692139 81908158106123070162018563180181853936899001652724284028354919772082656674531263 68776848460093246597991188966580072838377749283628053615667321078278332800674986 34836955296887819320091154814650187042142476705881310722447944642683286387297186 80326110572188774616596081647383105540198298481219494140660389443445798302148367 74384928506432757516512367789546579870827890454735754364703931677509602011553420 32335644278118701051847495347953883753033918029893901872888447417633312032191488 34746236959255205086744154606736078973863234701239322515710730795982758717722657 26780467634150811257892675947495895651510187934643552316588931723415687729819859 06475257769791027398824218166321081129344258734876563936280305291064332307261169 72079171530830146555149537289834362696705496446745344779681791547908286849315120 09654499981523685283435346310382344769874095951212674194856437256662507151301315 44926746904654542594435910120285032193730716691332728142519785532064608052436858 93663698820542170137641789450736306664795817728655473889715469600629850741487979 04921745880363735904456553649918897402519601220048284421167728354450201805032702 56322815775270131173505658699678834841721904863184250126068872096132796320920145 16177291471974496850964620059827457102133191211170871562465202246667433583734348 70510381224798762689582174115989559480727400083205785776974567157251036359248369 95955738458534454365900180461131195499412241042629288868653460121538406753370751 48366535287175783530402704721274766907538220338545132641000318993628602618278814 00765837524928800545288587519193968191620204107393850095027553136387602180749457 37833212643844955134275415615651678671259558519233926400305220022851466661204617 39889674866710880266438275038407778241284642298736755331057436760718850643341843 10789085504459281748652960238171364100266171687196609909030604354765210772244908 55182574480672829496248053453271761982057419641132205581528857839173020954117660 44649986005736835456418037708825602518588210188855819137844780353696648879094677 19206049607774298645079747783175780797722987956132754383236490025649041634850152 44132048398127596386865493668804060207011581421885124277214807174809648955334711 53614941348668339159009912870173392008377954973533535028461023648198101932601031 88814237898583254355130245993967885534183382493499137333648763178032562626315252 75186014899532879664926809234513882444868239515843135186921130742854447912462533 79122460440710384489787797786209815649434318699407741381527147327742459347773666 25532915471697416345206127970255246470680384289478188009467250886191345918962144 51934677919102633612738884259013827476833557236900583870653133944718409124066626 394978366914920767896729876939969396735
Pretty big number, isn't it?
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