Download Logic and Automata: History and Perspectives (Amsterdam by Jorg Flum, Erich Gradel, Thomas Wilke PDF

By Jorg Flum, Erich Gradel, Thomas Wilke

Mathematical common sense and automata thought are clinical disciplines with a essentially shut dating. The authors of Logic and Automata take the get together of the 60th birthday of Wolfgang Thomas to provide a tour d’horizon of automata conception and good judgment. The twenty papers during this quantity hide many various features of good judgment and automata thought, emphasizing the connections to different disciplines corresponding to video games, algorithms, and semigroup concept, in addition to discussing present demanding situations within the field. 

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First, we shall show that the problem is undecidable even when A, B and C are simple automata. 2 for the case when there are at least two processes that can be nondeterministic. Next, we shall consider the case when at most one of the processes can be nondeterministic. We shall show that the above problem is undecidable when only R can be nondeterministic, and when B can use either constraints or ↓↓ constrains. 2, but will also show that restricting our automata uniquely to constraints or to ↓↓ constraints does not change the decidability classification.

Im vim #. As R we take a process as depicted in Figure 3 50 A. Arnold and I. Walukiewicz P: α1 α2 D β β A R: α1 α2 β β D a1 d1 A i1 j1 D a2 d2 A D # Figure 3. # A # # -constraints. Intended shapes of P and R. where the path satisfying condition B2 has the form βui1 . . uim #, and the path satisfying B3 is βi1 . . im #. It is easy to see that P × R satisfies A. For the direction from left to right suppose that P and R are a solution to the problem. Consider a path of R labelled βΣ∗ # satisfying B2 and the path α1 βi1 ui1 .

O. de Abstract Continuous-time Markov decision processes (CTMDPs) are widely used for the control of queueing systems, epidemic and manufacturing processes. Various results on optimal schedulers for discounted and average reward optimality criteria in CTMDPs are known, but the typical game-theoretic winning objectives have received scant attention so far. This paper studies various sorts of reachability objectives for CTMDPs. The central result is that for any CTMDP, reward reachability objectives are dual to timed ones.

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