GOAL Extended Towards a Research Tool for Omega Automata and Temporal Logic
GOAL Extended:Towards a Research Tool for Omega Automata and Temporal Logic Yih-Kuen Tsay,Yu-Fang Chen,Ming-Hsien Tsai,Wen-Chin Chan,and
Chi-Jian Luo
Department of Information Management,National Taiwan University,Taiwan Abstract.This paper reports extensions to the GOAL tool that enable
it to become a research tool for omega automata and temporal logic.The
extensions include an expanded collection of translation,simpli?cation,
and complementation algorithms,a command-line mode which makes
GOAL functions accessible by programs,and utility functions for such
common tasks as?le format conversion,random formulae generation,
and statistics collection.
1Introduction
GOAL(https://www.wendangku.net/doc/1510115961.html,.tw)is a graphical interactive tool for de?n-ing and manipulatingω-automata,in particular B¨u chi automata,and temporal logic formulae.It was?rst formally introduced in[20].Two most useful and dis-tinctive functions of GOAL are(1)translation of quanti?ed propositional linear temporal logic(QPTL)formulae into equivalent B¨u chi automata and(2)equiv-alence test between two B¨u chi automata or between a B¨u chi automaton and a QPTL formula.With these and other utility functions,the GOAL tool may be used for educational purposes and for supplementing automata-theoretic model checkers such as SPIN[8].For example,the user may use GOAL to prepare a B¨u chi automaton diagram that is checked to be correct in that it is equivalent to another larger reference B¨u chi automaton or some easier-to-understand QPTL formula.
In this paper,we report extensions to GOAL that enable it to become a research tool forω-automata and temporal logic.We have at present focused on B¨u chi automata and PTL(which subsumes LTL).The extensions and their usage for supporting research are described in the next section.Table1sum-marizes the major algorithms implemented in GOAL.Though the number of supported functions does not actually increase,a larger collection of algorithms are very useful for various research purposes.In addition,several utility func-tions have been implemented for common tasks in experimentation such as(1) collecting statistic data and(2)generating random automata and temporal for-mulae.These functions allow researchers to test correctness of their translation This work was partially supported by the iCAST project sponsored by the National Science Council,Taiwan,under the Grant No.NSC96-3114-P-001-002-Y.
algorithm,collect comparison data,and,with GOAL’s graphical interface,vi-sually observe and manipulate automata generated from their algorithm.The extensions also enhance the original roles of GOAL as a learning/teaching tool
and as a supplementary model-checking tool.
Translation Complementation
Tableau*,Inc.Tableau[9],Temp.Tester[10],Safra*,WAPA[18],WAA[11],Piterman[13] GPVW[5],GPVW+[5],LTL2AUT[1],Simpli?cation
LTL2AUT+[19],LTL2BA[3],PLTL2BA[4]Simulation*,Pruning fair sets[15]
Table1.Major algorithms in GOAL.An*indicates that the algorithm had already
been implemented in earlier versions of GOAL[20].
2The Extensions for Supporting Research
In this section,we detail the extensions to GOAL and explain how they may be used for supporting research.
–Translation Algorithms:In addition to the Tableau algorithm[12],we have now implemented eight translation algorithms.Four(Tableau,Incre-
mental Tableau,Temporal Tester,and PLTL2BA)of the nine algorithms
originally support past operators.We have extended three more(GPVW,
LTL2AUT,and LTL2AUT+)to allow past operators.All these nine algo-
rithms are further extended to support quanti?cation on propositions.
As an illustration of usage,Table3summarizes the results of translating the
following two equivalent formulae into generalized B¨u chi automata by seven
algorithms:
1.?(3p→(?p U(q∧?p∧ (?p U r))))
2.?2(p→(?3(r∧? ?3q)))
Each formula is the negation of a formula stating that p must be triggered
by q and r with q occurring strictly before r.The?rst formula with only
future operators is taken from the Spec Patterns respository[16].
–Complementation and Simpli?cation Algorithms:In addition to Safra’s construction,GOAL now has another three complementation algorithms,in-
cluding complementation via weak alternating parity automata(WAPA)[18],
complementation via weak alternating automata(WAA)[11],and Piter-
man’s construction[13].Cross-checking greatly increases our con?dence in
the correctness of the di?erent complementation algorithms,which are di?-
cult,and hence the correctness of the language containment and equivalence
tests.GOAL applies simpli?cation algorithms to the input automata before
an equivalence test,and this substantially enhances the performance.Besides
the simulation-based method in[15],we have also implemented simpli?cation
heuristics based on pruning fair sets in the same work.
No.
Extended Extended Extended
Tableau GPVW GPVW+LTL2AUT LTL2AUT+LTL2BA PLTL2BA st tran acc st tran acc st tran acc st tran acc st tran acc st tran acc st tran acc
1.655503724561492881228412110518301331181
2.49396113551---92318171---15381
1.146831458113521134618271830114411
2.102617211---51015101---10231 Table
https://www.wendangku.net/doc/1510115961.html,parison of seven translation algorithms without and with simpli?cation. The column acc indicates the number of acceptance sets.
–The Command-Line Mode:This mode makes most of the GOAL func-tions accessible by programs or shell scripts.It therefore provides an interface between GOAL and external tools.Sample shell scripts that compare trans-lation algorithms and output the results as text?les are provided.They can be easily adapted to handle other di?erent tasks.
–Utility Functions:Utility functions are available for collecting statistic data(numbers of states,transitions,and acceptance sets)and for generating random automata and random temporal formulae.Outputs from external automata tools MoDeLLa[14]and LTL2Buchi[6]may also be converted to the GOAL File Format(GFF,which is an XML?le format designed to cover allω-automata)for further processing by GOAL.
We now describe a typical use case for the above functions,namely checking correctness of a translation algorithm.This task can be performed with high con?dence by comparing the results of the algorithm under test with(1) those of a large number of di?erent translation algorithms,(2)those of a reference algorithm,or(3)a set of reference answers,consisting of pairs of formulae and their equivalent B¨u chi automata.
We assume a reference algorithm.To carry out the correctness checking pro-cess,generate an adequate number of random temporal formulae and then apply the following procedure repeatedly for each formula f:
https://www.wendangku.net/doc/1510115961.html,e the reference algorithm to generate two automata A f and A?f that are
equivalent to f and?f respectively.
https://www.wendangku.net/doc/1510115961.html,e the algorithm under test to translate f into an automaton B.
3.Test if both A?f∩B and A f∩B are empty.
If all the emptiness tests succeed,then the algorithm should be correct.Oth-erwise,GOAL will produce counterexamples which can be run interactively on the automata to“see”what the problem might be.We developed our transla-tion algorithms in this manner.GOAL helped us to?nd some subtle bugs and possible room for improvement.
3Performance Evaluation and An Example Experiment We present an experiment that,on the one hand,evaluates the performance of GOAL and,on the other,demonstrates experimental comparative studies that may be conducted with GOAL.The experiment was run on an Intel Xeon 3.2GHz machine with2GB of memory allocated to the Java Virtual Machine.
States Transitions Time Timeout ?f to BA1629690651.0s0
Safra246111721175.7s6
Simpli?cation+Safra2077970722.1s+114.8s5
WAPA8919649022786346.3s51
Simpli?cation+WAPA882842524814.0s+202.9s27
WAA2920278703629.4s51
Simpli?cation+WAA188********.1s+167.3s27
Piterman181********.5s5
Simpli?cation+Piterman1531691623.4s+442.4s3
https://www.wendangku.net/doc/1510115961.html,parison of complementation algorithms without and with simpli?cation. Only successful runs are accounted in the accumulated States,Transitions,and Time.
In the experiment,we compared the four complementation algorithms imple-mented in GOAL without and with simpli?cation.Note that the performance of a complementation algorithm dictates the performance of the equivalence test function it supports.We generated300random PTL formulae with a length of5and translated them into B¨u chi automata as inputs using the LTL2AUT algorithm.None of the300formulae are valid or unsatis?able.The average size of the input automata is about5.4.We set a timeout of10minutes.From this experiment,we found that(1)Safra’s and Piterman’s algorithms perform much better than complementation via WAPA and complementation via WAA and(2)simpli?cation can signi?cantly speed up the complementation task,es-pecially complementation via WAPA and complementation via WAA.
4Remarks
The extension of GOAL will continue to include a few more complementation algorithms,for example[2].Another e?ort will be to include even more trans-lation algorithms,in particular those that utilize intermediary automata with acceptance conditions on transitions such as[17]and those that do simpli?cation while constructing automata on-the-?y[7].The fact that Safra’s and Piterman’s algorithms in average work better than complementation via WAPA and com-plementation via WAA is also worthy of further investigation. Acknowledgment.We thank Susan H.Rodger at Duke University for granting us the permission to use and modify the JFLAP source code.
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大学英语口语考试情景对话
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大学英语口语课教案
大学英语口语课教案
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1.master the basic vocabulary related to western wedding. 2.learn to describe the different manners between chinese and western customs. 3.learn the proper way to behave in western society. 本授课单元教学重点(main points of teaching)： 1.instruct students to speak and behave properly in western society concerning some important events. 2.analyze the different manners between chinese and western countries. 本授课单元教学难点(difficult points of teaching)： instruct the students to use cultural-related words to describe and compare the proper manners in chinese and western events.教学手段(teaching aids) multimedia (audios, videos, pictures, texts), blackboard. 本授课单元教学步骤及时间分配(teaching procedures and time allotment)： 1. warming-up activities (about 15 minutes) 1.1 role play: a typical western wedding (about 10 minutes) student are assigned the task in the previous class. they are asked to perform a typical western wedding. useful materials and information
最全大学英语口语情景对话
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大学英语口语对话稿子
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大学英语口语课堂游戏
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最全大学英语口语情景对话
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第一次做家务500字作文
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为父母做家务心得2 今天是星期天，我睡了个懒觉，九点钟才起来。下床一看，发现爸爸妈妈都出去了。吃完父母留给我的早餐后，望着脏兮兮的屋子，决定抓住这个机会锻炼一下自己。 我看了看灰尘很多的房间，准备先打扫房间。我拿来扫帚和撮箕，装着很在行的 样子，一甩一甩的，把灰尘都扬起来了。我呛得受不了，连忙打开窗户，灰尘全部随 着风飘出去了。 我又拿来拖把，把它弄得湿漉漉的，我专心致志地拖起来。因为地面太滑，我一 个踉跄，摔了个“狗啃泥”。过了一个小时，我坐在沙发上欣赏我的“杰作”：地板被打扫 的一尘不染，还闪着光呢。 这时，时钟已经指向了十一点，我肚子饿得咕咕叫，该煮饭了。我先淘米，把米 和水混在一起，不停地用手搅拌。淘干净后在电饭煲内放好水，插上插头，按上按钮。然后我从冰箱里拿出豆角，洗干净后，小心翼翼的切好放到锅里。我又往锅里倒了点 油和盐，炒起来。炒完豆角，我看了时间，急忙三步并两步跑到电饭煲旁，拔掉插头，慢慢的揭开锅盖，长出一口气，说：“还好没焦!” 等我做完菜，爸爸妈妈也回来了，他们看见我收拾好的房间，和桌子上的饭菜， 不停地说：“我们儿子长大了!”“哈哈哈……”全家沉浸在笑声当中。 这个星期天我做了一些力所能及的家务活，既能减轻父母的负担，又锻炼了我的 生活自理能力。做家务的感觉真好! 为父母做家务心得3 小时候，我们看着爸爸、妈妈在家里做家务活。那时，我又怎么会知道做家务是 如此不易啊! 有一天，我对爸爸、妈妈说道：“今天，由我来帮你们做家务吧!”爸爸、妈妈欣慰 地看着我，笑着说：“我们的儿子长大了。”首先我从客厅开始搞卫生。我拿起扫把把 客厅里的地扫干净，然后又用抹布把地板擦得一尘不染。 换过新的水之后，我又把桌子擦了一遍，那叫一个亮啊!搞完客厅，现在该打扫房 间以及阳台和厨房了。我心里想：天啊!光打扫一个客厅都这么费劲，想想爸爸、妈妈 是有多么不容易啊。