92 research outputs found
Isomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as
well as the existence of automorphisms of scattered word automatic linear
orders are undecidable. For the existence of automatic automorphisms of word
automatic linear orders, we determine the exact level of undecidability in the
arithmetical hierarchy
An optimal construction of Hanf sentences
We give the first elementary construction of equivalent formulas in Hanf
normal form. The triply exponential upper bound is complemented by a matching
lower bound
Infinite and Bi-infinite Words with Decidable Monadic Theories
We study word structures of the form where is either
or , is the natural linear ordering on and
is a predicate on . In particular we show:
(a) The set of recursive -words with decidable monadic second order
theories is -complete.
(b) Known characterisations of the -words with decidable monadic
second order theories are transfered to the corresponding question for
bi-infinite words.
(c) We show that such "tame" predicates exist in every Turing degree.
(d) We determine, for , the number of predicates
such that and
are indistinguishable.
Through these results we demonstrate similarities and differences between
logical properties of infinite and bi-infinite words
Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic
We investigate the relation between the theory of the iterations in the sense
of Shelah-Stupp and of Muchnik, resp., and the theory of the base structure for
several logics. These logics are obtained from the restriction of set
quantification in monadic second order logic to certain subsets like, e.g.,
finite sets, chains, and finite unions of chains. We show that these theories
of the Shelah-Stupp iteration can be reduced to corresponding theories of the
base structure. This fails for Muchnik's iteration
Weighted and unweighted trace automata
We reprove Droste & Gastin's characterisation from [3] of the behaviors of weighted trace automata by certain rational expressions. This proof shows how to derive their result on weighted trace automata as a corollary to the unweighted counterpart shown by Ochmański
Compatibility of Shelah and Stupp's and of Muchnik's iteration with fragments of monadic second order logic
We investigate the relation between the theory of the itera- tions in the sense of Shelah-Stupp and of Muchnik, resp., and the theory of the base structure for several logics. These logics are obtained from the restriction of set quantification in monadic second order logic to cer- tain subsets like, e.g., finite sets, chains, and finite unions of chains. We show that these theories of the Shelah-Stupp iteration can be reduced to corresponding theories of the base structure. This fails for Muchnik's iteration
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