1,062 research outputs found
Enumeration of minimal acyclic automata via generalized parking functions
We give an exact enumerative formula for the minimal acyclic deterministic
finite automata. This formula is obtained from a bijection between a family of
generalized parking functions and the transitions functions of acyclic
automata
Random Generation and Enumeration of Accessible Determinisitic Real-time Pushdown Automata
This papers presents a general framework for the uniform random generation of
deterministic real-time accessible pushdown automata. A polynomial time
algorithm to randomly generate a pushdown automaton having a fixed stack
operations total size is proposed. The influence of the accepting condition
(empty stack, final state) on the reachability of the generated automata is
investigated.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
FAdo and GUItar: tools for automata manipulation and visualization
Abstract. FAdo is an ongoing project which aims to provide a set of tools for symbolic manipulation of formal languages. To allow highlevel programming with complex data structures, easy prototyping of algorithms, and portability (to use in computer grid systems for example), are its main features. Our main motivation is the theoretical and experimental research, but we have also in mind the construction of a pedagogical tool for teaching automata theory and formal languages. For the graphical visualization and interactive manipulation a new interface application, GUItar, is being developed. In this paper, we describe the main components of the FAdo system as well as the basics of the graphical interface and editor, the export/import filters and its generic interface with external systems, such as FAdo.
On the Uniform Random Generation of Determinisitic Partially Ordered Automata using Monte Carlo Techniques
Partially ordered automata are finite automata admitting no simple loops of length greater than or equal to 2. In this paper we show how to randomly and uniformly generate deterministic accessible partially ordered automata using Monte-Carlo techniques
Asymptotics of Minimal Deterministic Finite Automata Recognizing a Finite Binary Language
We show that the number of minimal deterministic finite automata with n+1 states recognizing a finite binary language grows asymptotically for n ? ? like ?(n! 8? e^{3 a? n^{1/3}} n^{7/8}), where a? ? -2.338 is the largest root of the Airy function. For this purpose, we use a new asymptotic enumeration method proposed by the same authors in a recent preprint (2019). We first derive a new two-parameter recurrence relation for the number of such automata up to a given size. Using this result, we prove by induction tight bounds that are sufficiently accurate for large n to determine the asymptotic form using adapted Netwon polygons
Propagating Regular Counting Constraints
Constraints over finite sequences of variables are ubiquitous in sequencing
and timetabling. Moreover, the wide variety of such constraints in practical
applications led to general modelling techniques and generic propagation
algorithms, often based on deterministic finite automata (DFA) and their
extensions. We consider counter-DFAs (cDFA), which provide concise models for
regular counting constraints, that is constraints over the number of times a
regular-language pattern occurs in a sequence. We show how to enforce domain
consistency in polynomial time for atmost and atleast regular counting
constraints based on the frequent case of a cDFA with only accepting states and
a single counter that can be incremented by transitions. We also prove that the
satisfaction of exact regular counting constraints is NP-hard and indicate that
an incomplete algorithm for exact regular counting constraints is faster and
provides more pruning than the existing propagator from [3]. Regular counting
constraints are closely related to the CostRegular constraint but contribute
both a natural abstraction and some computational advantages.Comment: Includes a SICStus Prolog source file with the propagato
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