14 research outputs found
Improving the Upper Bound on the Length of the Shortest Reset Word
We improve the best known upper bound on the length of the shortest reset words of synchronizing automata. The new bound is slightly better than 114 n^3 / 685 + O(n^2). The Cerny conjecture states that (n-1)^2 is an upper bound. So far, the best general upper bound was (n^3-n)/6-1 obtained by J.-E. Pin and P. Frankl in 1982. Despite a number of efforts, it remained unchanged for about 35 years.
To obtain the new upper bound we utilize avoiding words.
A word is avoiding for a state q if after reading the word the automaton cannot be in q. We obtain upper bounds on the length of the shortest avoiding words, and using the approach of Trahtman from 2011 combined with the well-known Frankl theorem from 1982, we improve the general upper bound on the length of the shortest reset words.
For all the bounds, there exist polynomial algorithms finding a word of length not exceeding the bound
Implicit automata in typed -calculi II: streaming transducers vs categorical semantics
We characterize regular string transductions as programs in a linear
-calculus with additives. One direction of this equivalence is proved
by encoding copyless streaming string transducers (SSTs), which compute regular
functions, into our -calculus. For the converse, we consider a
categorical framework for defining automata and transducers over words, which
allows us to relate register updates in SSTs to the semantics of the linear
-calculus in a suitable monoidal closed category. To illustrate the
relevance of monoidal closure to automata theory, we also leverage this notion
to give abstract generalizations of the arguments showing that copyless SSTs
may be determinized and that the composition of two regular functions may be
implemented by a copyless SST. Our main result is then generalized from strings
to trees using a similar approach. In doing so, we exhibit a connection between
a feature of streaming tree transducers and the multiplicative/additive
distinction of linear logic.
Keywords: MSO transductions, implicit complexity, Dialectica categories,
Church encodingsComment: 105 pages, 24 figure
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Computer Aided Verification
The open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency