[CS@TUK] Questions and Answers - Recent questions and answers in * TF "Information Systems"
https://q2a.cs.uni-kl.de/qa/teaching-field-information-systems
Powered by Question2AnswerAnswered: Meaning of Confluence
https://q2a.cs.uni-kl.de/3329/meaning-of-confluence?show=3330#a3330
Given a DPN that works on channels x1,...,xn, the semantics is defined as a state transition system whose states are labeled with n streams, one for each variable x1,...,xn. If a node fires, it consumes values from some of these streams and adds values to other streams. If in some state, more than one node can fire, the question of confluence arises as discussed below.<br />
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We may formally define a relation s1->s2 that means that some nodes of the DPN fire and turn state s1 to state s2 by consuming and producing values for the streams in these states. Then, s1->*s2 mean that s2 can be reached from s1 by finitely many transitions, i.e., s1->s3->s4->...->s'->s2, and the epsilon means the reflexive closure of ->, i.e., x->εy means that either x=y or x->y holds.<br />
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A DPN is confluent iff for all x,y1,y2 with x->∗y1 and x->∗y2 there is a z with y1->∗ z and y2->∗z. Hence, it does not really matter whether we choose the firings x->∗y1 or the firings x->∗y2 since at the end, they can be joined into z.<br />
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See also pages 227 and the following in <a href="https://es.cs.uni-kl.de/publications/datarsg/Schn09.pdf" rel="nofollow">https://es.cs.uni-kl.de/publications/datarsg/Schn09.pdf</a>.* TF "Information Systems"https://q2a.cs.uni-kl.de/3329/meaning-of-confluence?show=3330#a3330Tue, 22 Nov 2022 16:16:32 +0000Answered: VRS Sheet 8 Q2 LTL Equivalence
https://q2a.cs.uni-kl.de/2719/vrs-sheet-8-q2-ltl-equivalence?show=2721#a2721
<p>Please repeat the question of the exercise sheet so that also students of later semesters can understand what we are discussing here. The question is that for a given LTL formulas S1 and S2, we should construct two LTL formulas φ1 and φ2 that satisfy the following requirements:</p><ol><li>φ1 and φ2 are not equivalent</li><li>φ1 and φ2 are both satisfiable</li><li>either φ1->S1&!S2 and φ2->S1&!S2 or φ1->!S1&S2 and φ2->!S1&S2are valid</li></ol><p>For the given formulas S1=[b WU [c WU a]] and S2=[b WU [c SU a]], you believe that [b WU [c WU a]] -> [b WU [c SU a]] would be valid, but that is not true. A counterexample is a single path where always !a&!b&c holds which obviously satisfies S1 but not S2. Note that [c WU a] holds here at every point of time, so that [b WU [c WU a]] is true at time 0, but [c SU a] is always false, and since b is also always false, S2 is false at initial time.</p><p>The formulas you suggest as a solution are φ1=G(!b&!a&c) and φ2=(!a&!b&c) & X(!a&b&c) & G(!b&!a&c). Formula φ1 holds exactly on the counterexample that I discussed above, so that the following is indeed valid:</p><p>G(!b&!a&c) -> [b WU [c WU a]] & ![b WU [c SU a]]</p><p>Also φ2->S1&!S2, i.e., the following formula is valid</p><p>(!a&!b&c) & X(!a&b&c) & G(!b&!a&c) -> [b WU [c WU a]] & ![b WU [c SU a]]</p><p>However, the above is valid since φ2 is not satisfiable: If G(!b&!a&c) holds at initial time, then also X(!b&!a&c) must hold which contradicts X(!a&b&c). </p><p>I guess you mean (!a&!b&c) & X((!a&b&c) & G(!b&!a&c)) as formula φ2, right?</p>* TF "Information Systems"https://q2a.cs.uni-kl.de/2719/vrs-sheet-8-q2-ltl-equivalence?show=2721#a2721Sun, 26 Jun 2022 09:00:09 +0000Answered: VRS Sheet 8 Q1 LTL Semantics
https://q2a.cs.uni-kl.de/2718/vrs-sheet-8-q1-ltl-semantics?show=2720#a2720
<p>Please repeat the question of the exercise sheet so that also students of later semesters can understand what we are discussing here. The question is that for a given LTL formula φ, we should construct two LTL formulas φ1 and φ2 that satisfy the following requirements:</p><ol><li>φ1 and φ2 are not equivalent</li><li>φ1 and φ2 are both satisfiable</li><li>φ1->!φ and φ2->!φ are valid</li></ol><p>For the given formula φ=[[c SU b] WU a], you suggest φ1=G(!a & b & !c) and φ2=G(!a & b & !c) which does obviously violate the first requirement: The formulas are even syntactically the same, so they are definitely equivalent. </p><p>For the second formula φ=[c SB [a SB b]], you suggest φ1=G(a & !b & !c) and φ2=G(!a & !b & c) which are satisfiable and not equivalent. Also, φ1->!φ is valid, but φ2->!φ is not valid: A counterexample is a single path where always !a&!b&c holds which obiviously satisfies φ2 but also satisfies φ.</p><p></p>* TF "Information Systems"https://q2a.cs.uni-kl.de/2718/vrs-sheet-8-q1-ltl-semantics?show=2720#a2720Sun, 26 Jun 2022 08:43:06 +0000Answered: VRS Sheet 7 Q2.b From Automaton Determinization 2
https://q2a.cs.uni-kl.de/2712/vrs-sheet-7-q2-b-from-automaton-determinization-2?show=2714#a2714
It is mentioned in the exercise text. You should enter something as follows: <br />
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labels 0:s1; 1:s2,s3; 2:; 3:s0,s1,s2; // encode Q<br />
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labels 0:; 1:s2,s3; 2:; 3:s2; // encode Qf<br />
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init 0,1;<br />
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transitions (0,{a},,1); (0,{},,2); (1,{},,3); (3,{a},,3); (3,{},,3);<br />
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accept 2,3;<br />
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The labels define the sets of states that form the pairs (Q,Qf) of the breakpoint construction.* TF "Information Systems"https://q2a.cs.uni-kl.de/2712/vrs-sheet-7-q2-b-from-automaton-determinization-2?show=2714#a2714Sun, 19 Jun 2022 09:05:19 +0000Answered: VRS Sheet 5 Q1.b From FSMs to Kripke Structures 1
https://q2a.cs.uni-kl.de/2676/vrs-sheet-5-q1-b-from-fsms-to-kripke-structures-1?show=2677#a2677
This is because of a bug in the exercise correction tool that is currently fixed. Your answer is correct, so please ask the tutor to give you the points.* TF "Information Systems"https://q2a.cs.uni-kl.de/2676/vrs-sheet-5-q1-b-from-fsms-to-kripke-structures-1?show=2677#a2677Thu, 02 Jun 2022 12:30:41 +0000Answered: VRS Sheet 4 Q2.a from FSMs to Kripke Structures 2
https://q2a.cs.uni-kl.de/2669/vrs-sheet-4-q2-a-from-fsms-to-kripke-structures-2?show=2670#a2670
<p>The transition <span style="font-family:Helvetica,Arial,sans-serif; font-size:14.000000953674316px">(2,{a},{!0},2) does not make sense. I guess you mean </span><span style="font-family:Helvetica,Arial,sans-serif; font-size:14.000000953674316px">(2,{a},{},2).</span></p>* TF "Information Systems"https://q2a.cs.uni-kl.de/2669/vrs-sheet-4-q2-a-from-fsms-to-kripke-structures-2?show=2670#a2670Sun, 29 May 2022 11:32:39 +0000Answered: [VRS] Sheet 4 Q1 from Semantics of Predecessors and Successors
https://q2a.cs.uni-kl.de/2667/vrs-sheet-q1-from-semantics-of-predecessors-and-successors?show=2668#a2668
Well, you should fill out the mentioned table by writing there either one of the numbers 1,...,6 which means one of the six states defined in the problem description. For instance, since pre∃(S) = S\deadends holds, the given entry in the table is 6. Hint: there is a slide in the chapter on Transition Systems that lists all of these state set.* TF "Information Systems"https://q2a.cs.uni-kl.de/2667/vrs-sheet-q1-from-semantics-of-predecessors-and-successors?show=2668#a2668Sun, 29 May 2022 10:55:45 +0000Answered: [VRS] Sheet 4 Q2 from FSM to Kripke
https://q2a.cs.uni-kl.de/2662/vrs-sheet-4-q2-from-fsm-to-kripke?show=2666#a2666
It is already answered in the comments.* TF "Information Systems"https://q2a.cs.uni-kl.de/2662/vrs-sheet-4-q2-from-fsm-to-kripke?show=2666#a2666Sun, 29 May 2022 09:36:06 +0000