27 research outputs found
Preimage problems for deterministic finite automata
Given a subset of states of a deterministic finite automaton and a word
, the preimage is the subset of all states mapped to a state in by the
action of . We study three natural problems concerning words giving certain
preimages. The first problem is whether, for a given subset, there exists a
word \emph{extending} the subset (giving a larger preimage). The second problem
is whether there exists a \emph{totally extending} word (giving the whole set
of states as a preimage)---equivalently, whether there exists an
\emph{avoiding} word for the complementary subset. The third problem is whether
there exists a \emph{resizing} word. We also consider variants where the length
of the word is upper bounded, where the size of the given subset is restricted,
and where the automaton is strongly connected, synchronizing, or binary. We
conclude with a summary of the complexities in all combinations of the cases
Solving One Variable Word Equations in the Free Group in Cubic Time
A word equation with one variable in a free group is given as , where
both and are words over the alphabet of generators of the free group
and , for a fixed variable . An element of the free group is a
solution when substituting it for yields a true equality (interpreted in
the free group) of left- and right-hand sides. It is known that the set of all
solutions of a given word equation with one variable is a finite union of sets
of the form , where are reduced words over the alphabet of generators, and a polynomial-time
algorithm (of a high degree) computing this set is known. We provide a cubic
time algorithm for this problem, which also shows that the set of solutions
consists of at most a quadratic number of the above-mentioned sets. The
algorithm uses only simple tools of word combinatorics and group theory and is
simple to state. Its analysis is involved and focuses on the combinatorics of
occurrences of powers of a word within a larger word.Comment: 52 pages, accepted to STACS 202
Complexity of Preimage Problems for Deterministic Finite Automata
Given a subset of states S of a deterministic finite automaton and a word w, the preimage is the subset of all states that are mapped to a state from S by the action of w. We study the computational complexity of three problems related to the existence of words yielding certain preimages, which are especially motivated by the theory of synchronizing automata. The first problem is whether, for a given subset, there exists a word extending the subset (giving a larger preimage). The second problem is whether there exists a word totally extending the subset (giving the whole set of states) - it is equivalent to the problem whether there exists an avoiding word for the complementary subset. The third problem is whether there exists a word resizing the subset (giving a preimage of a different size). We also consider the variants of the problem where an upper bound on the length of the word is given in the input. Because in most cases our problems are computationally hard, we additionally consider parametrized complexity by the size of the given subset. We focus on the most interesting cases that are the subclasses of strongly connected, synchronizing, and binary automata
Attainable Values of Reset Thresholds
An automaton is synchronizing if there exists a word that sends all states of the automaton to a single state. The reset threshold is the length of the shortest such word. We study the set RT_n of attainable reset thresholds by automata with n states. Relying on constructions of digraphs with known local exponents we show that the intervals [1, (n^2-3n+4)/2] and
[(p-1)(q-1), p(q-2)+n-q+1], where 2 n, gcd(p,q)=1, belong to RT_n, even if restrict our attention to strongly connected automata. Moreover, we prove that in this case the smallest value that does not belong to RT_n is at least n^2 - O(n^{1.7625} log n / log log n).
This value is increased further assuming certain conjectures about the gaps between consecutive prime numbers.
We also show that any value smaller than n(n-1)/2 is attainable by an automaton with a sink state and any value smaller than n^2-O(n^{1.5}) is attainable in general case.
Furthermore, we solve the problem of existence of slowly synchronizing automata over an arbitrarily large alphabet, by presenting for every fixed size of the alphabet an infinite series of irreducibly synchronizing automata with the reset threshold n^2-O(n)
Synchronizing Strongly Connected Partial DFAs
We study synchronizing partial DFAs, which extend the classical concept of
synchronizing complete DFAs and are a special case of synchronizing unambiguous
NFAs. A partial DFA is called synchronizing if it has a word (called a reset
word) whose action brings a non-empty subset of states to a unique state and is
undefined for all other states. While in the general case the problem of
checking whether a partial DFA is synchronizing is PSPACE-complete, we show
that in the strongly connected case this problem can be efficiently reduced to
the same problem for a complete DFA. Using combinatorial, algebraic, and formal
languages methods, we develop techniques that relate main synchronization
problems for strongly connected partial DFAs with the same problems for
complete DFAs. In particular, this includes the \v{C}ern\'{y} and the rank
conjectures, the problem of finding a reset word, and upper bounds on the
length of the shortest reset words of literal automata of finite prefix codes.
We conclude that solving fundamental synchronization problems is equally hard
in both models, as an essential improvement of the results for one model
implies an improvement for the other.Comment: Full version of the paper at STACS 202
Mechanical thrombectomy in acute stroke – Five years of experience in Poland
Objectives
Mechanical thrombectomy (MT) is not reimbursed by the Polish public health system. We present a description of 5 years of experience with MT in acute stroke in Comprehensive Stroke Centers (CSCs) in Poland.
Methods and results
We retrospectively analyzed the results of a structured questionnaire from 23 out of 25 identified CSCs and 22 data sets that include 61 clinical, radiological and outcome measures.
Results
Most of the CSCs (74%) were founded at University Hospitals and most (65.2%) work round the clock. In 78.3% of them, the working teams are composed of neurologists and neuro-radiologists. All CSCs perform CT and angio-CT before MT. In total 586 patients were subjected to MT and data from 531 of them were analyzed. Mean time laps from stroke onset to groin puncture was 250±99min. 90.3% of the studied patients had MT within 6h from stroke onset; 59.3% of them were treated with IV rt-PA prior to MT; 15.1% had IA rt-PA during MT and 4.7% – emergent stenting of a large vessel. M1 of MCA was occluded in 47.8% of cases. The Solitaire device was used in 53% of cases. Successful recanalization (TICI2b–TICI3) was achieved in 64.6% of cases and 53.4% of patients did not experience hemorrhagic transformation. Clinical improvement on discharge was noticed in 53.7% of cases, futile recanalization – in 30.7%, mRS of 0–2 – in 31.4% and mRS of 6 in 22% of cases.
Conclusion
Our results can help harmonize standards for MT in Poland according to international guidelines