8 research outputs found
Quotient Complexity Of Closed Languages
The final publication is available at Springer via http://dx.doi.org/10.1007/s00224-013-9515-7A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in an analogous way, where by factor we mean contiguous subsequence, and by subword we mean scattered subsequence. We study the state complexity (which we prefer to call quotient complexity) of operations on prefix-, suffix-, factor-, and subword-closed languages. We find tight upper bounds on the complexity of the subword-closure of arbitrary languages, and on the complexity of boolean operations, concatenation, star, and reversal in each of the four classes of closed languages. We show that repeated applications of positive closure and complement to a closed language result in at most four distinct languages, while Kleene closure and complement give at most eight.Natural Sciences and Engineering Research Council of Canada [OGP0000871]VEGA grant [2/0183/11][APVV-0035-10
Attribute Exploration of Gene Regulatory Processes
This thesis aims at the logical analysis of discrete processes, in particular
of such generated by gene regulatory networks. States, transitions and
operators from temporal logics are expressed in the language of Formal Concept
Analysis. By the attribute exploration algorithm, an expert or a computer
program is enabled to validate a minimal and complete set of implications, e.g.
by comparison of predictions derived from literature with observed data. Here,
these rules represent temporal dependencies within gene regulatory networks
including coexpression of genes, reachability of states, invariants or possible
causal relationships. This new approach is embedded into the theory of
universal coalgebras, particularly automata, Kripke structures and Labelled
Transition Systems. A comparison with the temporal expressivity of Description
Logics is made. The main theoretical results concern the integration of
background knowledge into the successive exploration of the defined data
structures (formal contexts). Applying the method a Boolean network from
literature modelling sporulation of Bacillus subtilis is examined. Finally, we
developed an asynchronous Boolean network for extracellular matrix formation
and destruction in the context of rheumatoid arthritis.Comment: 111 pages, 9 figures, file size 2.1 MB, PhD thesis University of
Jena, Germany, Faculty of Mathematics and Computer Science, 2011. Online
available at http://www.db-thueringen.de/servlets/DocumentServlet?id=1960
Mathematical linguistics
but in fact this is still an early draft, version 0.56, August 1 2001. Please d
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
Efficient reduction of nondeterministic automata with application to language inclusion testing
We present efficient algorithms to reduce the size of nondeterministic
B\"uchi word automata (NBA) and nondeterministic finite word automata (NFA),
while retaining their languages. Additionally, we describe methods to solve
PSPACE-complete automata problems like language universality, equivalence, and
inclusion for much larger instances than was previously possible (
states instead of 10-100). This can be used to scale up applications of
automata in formal verification tools and decision procedures for logical
theories. The algorithms are based on new techniques for removing transitions
(pruning) and adding transitions (saturation), as well as extensions of classic
quotienting of the state space. These techniques use criteria based on
combinations of backward and forward trace inclusions and simulation relations.
Since trace inclusion relations are themselves PSPACE-complete, we introduce
lookahead simulations as good polynomial time computable approximations
thereof. Extensive experiments show that the average-case time complexity of
our algorithms scales slightly above quadratically. (The space complexity is
worst-case quadratic.) The size reduction of the automata depends very much on
the class of instances, but our algorithm consistently reduces the size far
more than all previous techniques. We tested our algorithms on NBA derived from
LTL-formulae, NBA derived from mutual exclusion protocols and many classes of
random NBA and NFA, and compared their performance to the well-known automata
tool GOAL.Comment: 69 pages. arXiv admin note: text overlap with arXiv:1210.662
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems