By Gabriele Puppis
Since 2002, FoLLI awards an annual prize for an excellent dissertation within the fields of good judgment, Language, and data. This booklet relies at the Ph.D. thesis of Gabriele Puppis, who used to be the winner of the E.W. Beth dissertation award for 2007.
Puppis' thesis specializes in common sense and Computation and, extra in particular, on automata-based decidability thoughts for time granularity and on a brand new procedure for determining Monadic moment Order theories of bushes. the implications awarded characterize an important step in the direction of a greater realizing of the alterations in granularity degrees that people make so simply in cognition of time, house, and different phenomena, while their logical and computational constitution poses tough conceptual and computational challenges.
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Extra resources for Automata for Branching and Layered Temporal Structures: An Investigation into Regularities of Infinite Transition Systems
Cover, covered-by) conversion of T . The above arguments show that granule conversions between time granularities can be performed by exploiting basic algorithms on NCSSA. , the size) of the input NCSSA. 3 Compact and Tractable Representations 39 The Equivalence Problem We now focus our attention on the equivalence problem for NCSSA, namely, the problem of deciding whether two given NCSSA recognize the same (ﬁnite or inﬁnite) word. As a matter of fact, solving such a problem makes it possible to check whether two given NCCSA represent the same time granularity and hence to choose the most compact, or the most suitable, representation.
As a preliminary result, we establish the following technical lemma. Lemma 5. , n 0), there is a decomposable NCSSA Prefix(A, n) that recognizes the preﬁx w[1, n] of w and such that Prefix(A, n) A . Proof. By Proposition 4, we know that there is a decomposable NCSSA A which is equivalent to A and satisﬁes A A . We deﬁne the NCSSA Prefix(A, n) by exploiting induction on the decomposition structure of A . We only consider the non-trivial cases, namely, the cases of non-empty NCSSA. 1. Suppose that A = AppendChar(a, B).
This shows that ΓA can be given the status of a well-founded partial order over the set of states of A. Such a partial order immediately suggests an induction principle, called γ-induction, which can be used for both deﬁnitions and proofs. 7. , 2), the nesting relation ΓA is the set (s1 , s2 ), (s0 , s3 ), (s2 , s3 ) , + and its transitive closure ΓA consists of all pairs in ΓA plus the pair (s1 , s3 ). 1b) (here, for the sake of simplicity, we assume that w1 w2 = w1 and wω 1 = w1 whenever w1 is an inﬁnite word).
Automata for Branching and Layered Temporal Structures: An Investigation into Regularities of Infinite Transition Systems by Gabriele Puppis