480 research outputs found
Deterministic blow-ups of minimal NFA\u27s
The paper treats the question whether there
always exists a minimal nondeterministic finite automaton of n states whose equivalent minimal deterministic finite automaton has α states for any integers n and α with n ≤ α ≤ 2n.
Partial answers to this question were given by Iwama, Kambayashi, and Takaki (2000) and by Iwama, Matsuura, and Paterson (2003).
In the present paper, the question is completely solved by presenting appropriate automata for all values of n and α. However,
in order to give an explicit construction of the automata, we increase the input alphabet to exponential sizes. Then we prove that 2n letters would be sufficient but we describe the related automata only implicitly. In the last section, we investigate the above question for automata over binary and unary alphabets
Patient data management in hospital information system Clinicom
Nemocniční informační systémy slouží k ukládání pacientských dat a k jejich sdílení. Mají několik výhod. Lékaři mají okamžitě přístupnou anamnézu, která pomáhá k rychlejší diagnostice, zabraňuje nadbytečnému plýtvání léky a duplicitním vyšetřením. Cílem mé bakalářské práce bylo vytvoření dálkového přístupu k nemocničnímu informačnímu systému Clinicom prostřednictvím internetu. Data jsou v informačním systému spravována databázovým systémem Caché. Z této databáze byly informace získávány pomocí SQL dotazů. Pro prezentaci dat na internetu bylo navrženo a realizováno uživatelské rozhraní v programovacím jazyce PHP, které umožňuje vzdálenou správu databáze systému Clinicom.Hospital information systems to store patient data and to share them. Have several advantages. Doctors are immediately accessible to history, which helps to quickly diagnose, prevent unnecessary wastage of drugs and duplicate tests. The goal of this work was to develop remote access to hospital information system CLINICOM via the Internet. The data in the information system managed by the database system Caché. From this database information was obtained using SQL queries. For the presentation of data on the Internet was designed and implemented user interface in the PHP programming language, which enables remote database management system CLINICOM.
Quotient Complexity of Regular Languages
The past research on the state complexity of operations on regular languages
is examined, and a new approach based on an old method (derivatives of regular
expressions) is presented. Since state complexity is a property of a language,
it is appropriate to define it in formal-language terms as the number of
distinct quotients of the language, and to call it "quotient complexity". The
problem of finding the quotient complexity of a language f(K,L) is considered,
where K and L are regular languages and f is a regular operation, for example,
union or concatenation. Since quotients can be represented by derivatives, one
can find a formula for the typical quotient of f(K,L) in terms of the quotients
of K and L. To obtain an upper bound on the number of quotients of f(K,L) all
one has to do is count how many such quotients are possible, and this makes
automaton constructions unnecessary. The advantages of this point of view are
illustrated by many examples. Moreover, new general observations are presented
to help in the estimation of the upper bounds on quotient complexity of regular
operations
State Complexity of Reversals of Deterministic Finite Automata with Output
We investigate the worst-case state complexity of reversals of deterministic
finite automata with output (DFAOs). In these automata, each state is assigned
some output value, rather than simply being labelled final or non-final. This
directly generalizes the well-studied problem of determining the worst-case
state complexity of reversals of ordinary deterministic finite automata. If a
DFAO has states and possible output values, there is a known upper
bound of for the state complexity of reversal. We show this bound can be
reached with a ternary input alphabet. We conjecture it cannot be reached with
a binary input alphabet except when , and give a lower bound for the
case . We prove that the state complexity of reversal depends
solely on the transition monoid of the DFAO and the mapping that assigns output
values to states.Comment: 18 pages, 3 tables. Added missing affiliation/funding informatio
Complexity in Prefix-Free Regular Languages
We examine deterministic and nondeterministic state complexities of regular
operations on prefix-free languages. We strengthen several results by providing
witness languages over smaller alphabets, usually as small as possible. We next
provide the tight bounds on state complexity of symmetric difference, and
deterministic and nondeterministic state complexity of difference and cyclic
shift of prefix-free languages.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Operations on Boolean and Alternating Finite Automata
We examine the complexity of basic regular operations on languages
represented by Boolean and alternating finite automata. We get tight upper
bounds m+n and m+n+1 for union, intersection, and difference, 2^m+n and 2^m+n+1
for concatenation, 2^n+n and 2^n+n+1 for square, m and m+1 for left quotient,
2^m and 2^m+1 for right quotient. We also show that in both models, the
complexity of complementation and symmetric difference is n and m+n,
respectively, while the complexity of star and reversal is 2^n. All our
witnesses are described over a unary or binary alphabets, and whenever we use a
binary alphabet, it is always optimal.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Operations on Automata with All States Final
We study the complexity of basic regular operations on languages represented
by incomplete deterministic or nondeterministic automata, in which all states
are final. Such languages are known to be prefix-closed. We get tight bounds on
both incomplete and nondeterministic state complexity of complement,
intersection, union, concatenation, star, and reversal on prefix-closed
languages.Comment: In Proceedings AFL 2014, arXiv:1405.527
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