472 research outputs found
A split-based incremental deterministic automata minimization algorithm
The final publication is available at Springer via http://dx.doi.org/10.1007/s00224-014-9588-y.
La fecha de publicación corresponde a la versión First OnlineWe here study previous results due to Hopcroft and Almeida et al. to
propose an incremental split-based deterministic automata minimization algorithm
whose average running-time does not depend on the size of the alphabet. The experimentation
carried out shows that our proposal outperforms the algorithms studied
whenever the automata have more than a (quite small) number of states and symbols.García Gómez, P.; Vázquez-De-Parga Andrade, M.; Velasco, JA.; López Rodríguez, D. (2014). A split-based incremental deterministic automata minimization algorithm. Theory of Computing Systems. 1-18. doi:10.1007/s00224-014-9588-y118Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley Publishing Company (1979)Watson, B.W., Daciuk, J.: An efficient incremental DFA minimization algorithm. Nat. Lang. Eng. 9(1), 49–64 (2003)Almeida, M., Moreira, N., Reis, R.: Incremental DFA minimisation. In: Domaratzki, M., Salomaa, K. (eds.) CIAA, of Lecture Notes in Computer Science, vol. 6482, pp 39–48. Springer (2010)Hopcroft, J.E.: An n ⋅ log n algorithm for minimizing states in a finite automaton. Technical report, Stanford, University, Stanford (1971)Moore, E.F.: Gedanken experiments on sequential machines. In: Shannon, C.E., Mc-Carthy, J. (eds.) Automata Studies. Princeton Universty Press, Princeton (1956)Berstel, J., Boasson, L., Carton, O., Fagnot, I.: Automata: from Mathematics to Applications, chapter Minimization of automata. European Mathematical Society. (arXiv: 1010.5318v3. ) To appear.David, J.: Average complexity of Moore’s and Hopcroft’s algorithms. Theor. Comput. Sci. 417, 50–65 (2012)Almeida, M., Moreira, N., Reis, R.: Aspects of enumeration and generation with a string automata representation. In: Leung, H., Pighizzini, G. (eds.) DCFS, pp 58–69. New Mexico State University, Las Cruces (2006)Gries, D.: Describing an algorithm by Hopcroft. Acta Informatica 2, 97–109 (1973)Aho, A., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company (1974)Blum, N.: A O ( n log n ) implementation of the standard method for minimizing n-state finite automata. Inf. Process. Lett. 57, 65–69 (1996)Knuutila, T.: Re-describing an algorithm by Hopcroft. Theor. Comput. Sci. 250, 333–363 (2001)Veanes, M.: Minimization of symbolic automata. Technical report, Microsoft Research, MSR-TR-2013-48 (2013)Lothaire, M.: Applied Combinatorics on Words chap. 1. Cambridge University Press, Cambridge (2005
On minimizing deterministic tree automata
We present two algorithms for minimizing deterministic frontier-to-root tree automata (dfrtas) and compare them with their string counterparts. The presentation is incremental, starting out from definitions of minimality of automata and state equivalence, in the style of earlier algorithm taxonomies by the authors. The first algorithm is the classical one, initially presented by Brainerd in the 1960s and presented (sometimes imprecisely) in standard texts on tree language theory ever since. The second algorithm is completely new. This algorithm, essentially representing the generalization to ranked trees of the string algorithm presented by Watson and Daciuk, incrementally minimizes a dfrta. As a result, intermediate results of the algorithm can be used to reduce the initial automaton’s size. This makes the algorithm useful in situations where running time is restricted (for example, in real-time applications). We also briefly sketch how a concurrent specification of the algorithm in CSP can be obtained from an existing specification for the dfa case
On minimizing deterministic tree automata
We present two algorithms for minimizing deterministic frontier-to-root tree automata (dfrtas) and compare them with their string counterparts. The presentation is incremental, starting out from definitions of minimality of automata and state equivalence, in the style of earlier algorithm taxonomies by the authors. The first algorithm is the classical one, initially presented by Brainerd in the 1960s and presented (sometimes imprecisely) in standard texts on tree language theory ever since. The second algorithm is completely new. This algorithm, essentially representing the generalization to ranked trees of the string algorithm presented by Watson and Daciuk, incrementally minimizes a dfrta. As a result, intermediate results of the algorithm can be used to reduce the initial automaton’s size. This makes the algorithm useful in situations where running time is restricted (for example, in real-time applications). We also briefly sketch how a concurrent specification of the algorithm in CSP can be obtained from an existing specification for the dfa case
CAIR: Using Formal Languages to Study Routing, Leaking, and Interception in BGP
The Internet routing protocol BGP expresses topological reachability and
policy-based decisions simultaneously in path vectors. A complete view on the
Internet backbone routing is given by the collection of all valid routes, which
is infeasible to obtain due to information hiding of BGP, the lack of
omnipresent collection points, and data complexity. Commonly, graph-based data
models are used to represent the Internet topology from a given set of BGP
routing tables but fall short of explaining policy contexts. As a consequence,
routing anomalies such as route leaks and interception attacks cannot be
explained with graphs.
In this paper, we use formal languages to represent the global routing system
in a rigorous model. Our CAIR framework translates BGP announcements into a
finite route language that allows for the incremental construction of minimal
route automata. CAIR preserves route diversity, is highly efficient, and
well-suited to monitor BGP path changes in real-time. We formally derive
implementable search patterns for route leaks and interception attacks. In
contrast to the state-of-the-art, we can detect these incidents. In practical
experiments, we analyze public BGP data over the last seven years
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efficient
implementation of a large range of basic operations on simplicial complexes. In
this paper, we show how to optimally compress the Simplex Tree while retaining
its functionalities. In addition, we propose two new data structures called the
Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the
compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List
under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201
Regular Languages meet Prefix Sorting
Indexing strings via prefix (or suffix) sorting is, arguably, one of the most
successful algorithmic techniques developed in the last decades. Can indexing
be extended to languages? The main contribution of this paper is to initiate
the study of the sub-class of regular languages accepted by an automaton whose
states can be prefix-sorted. Starting from the recent notion of Wheeler graph
[Gagie et al., TCS 2017]-which extends naturally the concept of prefix sorting
to labeled graphs-we investigate the properties of Wheeler languages, that is,
regular languages admitting an accepting Wheeler finite automaton.
Interestingly, we characterize this family as the natural extension of regular
languages endowed with the co-lexicographic ordering: when sorted, the strings
belonging to a Wheeler language are partitioned into a finite number of
co-lexicographic intervals, each formed by elements from a single Myhill-Nerode
equivalence class. Moreover: (i) We show that every Wheeler NFA (WNFA) with
states admits an equivalent Wheeler DFA (WDFA) with at most
states that can be computed in time. This is in sharp contrast with
general NFAs. (ii) We describe a quadratic algorithm to prefix-sort a proper
superset of the WDFAs, a -time online algorithm to sort acyclic
WDFAs, and an optimal linear-time offline algorithm to sort general WDFAs. By
contribution (i), our algorithms can also be used to index any WNFA at the
moderate price of doubling the automaton's size. (iii) We provide a
minimization theorem that characterizes the smallest WDFA recognizing the same
language of any input WDFA. The corresponding constructive algorithm runs in
optimal linear time in the acyclic case, and in time in the
general case. (iv) We show how to compute the smallest WDFA equivalent to any
acyclic DFA in nearly-optimal time.Comment: added minimization theorems; uploaded submitted version; New version
with new results (W-MH theorem, linear determinization), added author:
Giovanna D'Agostin
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