ترغب بنشر مسار تعليمي؟ اضغط هنا

Closure Properties of Locally Finite Omega Languages

159   0   0.0 ( 0 )
 نشر من قبل Olivier Finkel
 تاريخ النشر 2008
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English
 تأليف Olivier Finkel




اسأل ChatGPT حول البحث

Locally finite omega languages were introduced by Ressayre in [Journal of Symbolic Logic, Volume 53, No. 4, p.1009-1026]. They generalize omega languages accepted by finite automata or defined by monadic second order sentences. We study here closure properties of the family LOC_omega of locally finite omega languages. In particular we show that the class LOC_omega is neither closed under intersection nor under complementation, giving an answer to a question of Ressayre.



قيم البحث

اقرأ أيضاً

173 - Olivier Finkel 2017
We prove that $omega$-languages of (non-deterministic) Petri nets and $omega$-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of $omega$-languages of (non-determinist ic) Petri nets are equal to the Borel and Wadge hierarchies of the class of $omega$-languages of (non-deterministic) Turing machines which also form the class of effective analytic sets. In particular, for each non-null recursive ordinal $alpha < omega_1^{{rm CK}} $ there exist some ${bf Sigma}^0_alpha$-complete and some ${bf Pi}^0_alpha$-complete $omega$-languages of Petri nets, and the supremum of the set of Borel ranks of $omega$-languages of Petri nets is the ordinal $gamma_2^1$, which is strictly greater than the first non-recursive ordinal $omega_1^{{rm CK}}$. We also prove that there are some ${bf Sigma}_1^1$-complete, hence non-Borel, $omega$-languages of Petri nets, and that it is consistent with ZFC that there exist some $omega$-languages of Petri nets which are neither Borel nor ${bf Sigma}_1^1$-complete. This answers the question of the topological complexity of $omega$-languages of (non-deterministic) Petri nets which was left open in [DFR14,FS14].
259 - Olivier Finkel 2020
The $omega$-power of a finitary language L over a finite alphabet $Sigma$ is the language of infinite words over $Sigma$ defined by L $infty$ := {w 0 w 1. .. $in$ $Sigma$ $omega$ | $forall$i $in$ $omega$ w i $in$ L}. The $omega$-powers appear very na turally in Theoretical Computer Science in the characterization of several classes of languages of infinite words accepted by various kinds of automata, like B{u}chi automata or B{u}chi pushdown automata. We survey some recent results about the links relating Descriptive Set Theory and $omega$-powers.
235 - Olivier Finkel 2008
We study the links between the topological complexity of an omega context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free languages which ar e recognized by Buchi pushdown automata have a maximum degree of ambiguity. This result implies that degrees of ambiguity are really not preserved by the operation of taking the omega power of a finitary context free language. We prove also that taking the adherence or the delta-limit of a finitary language preserves neither unambiguity nor inherent ambiguity. On the other side we show that methods used in the study of omega context free languages can also be applied to study the notion of ambiguity in infinitary rational relations accepted by Buchi 2-tape automata and we get first results in that direction.
157 - Olivier Finkel 2012
An {omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {omega}-languages, i.e. the class of {omega}-languages accepted by Turing machines with a Buchi acceptance condition, which is also the class {Sigma}11 of (effective) analytic subsets of X{omega} for some finite alphabet X. We investigate here the notion of ambiguity for recursive {omega}-languages with regard to acceptance by Buchi Turing machines. We first present in detail essentials on the literature on {omega}-languages accepted by Turing Machines. Then we give a complete and broad view on the notion of ambiguity and unambiguity of Buchi Turing machines and of the {omega}-languages they accept. To obtain our new results, we make use of results and methods of effective descriptive set theory.
158 - Olivier Finkel 2008
We consider the set of infinite real traces, over a dependence alphabet (Gamma, D) with no isolated letter, equipped with the topology induced by the prefix metric. We then prove that all rational languages of infinite real traces are analytic sets a nd that there exist some rational languages of infinite real traces which are analytic but non Borel sets, and even Sigma^1_1-complete, hence of maximum possible topological complexity.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا