Algorithms for finding patterns in strings
Handbook of theoretical computer science (vol. A)
Digital images and formal languages
Handbook of formal languages, vol. 3
On the Determinization of Weighted Finite Automata
SIAM Journal on Computing
Nontraditional Applications of Automata Theory
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Efficient algorithms for testing the twins property
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Finite-state transducers in language and speech processing
Computational Linguistics
Planning Algorithms
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Finite automata and their decision problems
IBM Journal of Research and Development
Reasoning about online algorithms with weighted automata
ACM Transactions on Algorithms (TALG)
What's decidable about weighted automata?
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Verifying quantitative properties using bound functions
CHARME'05 Proceedings of the 13 IFIP WG 10.5 international conference on Correct Hardware Design and Verification Methods
Making weighted containment feasible: a heuristic based on simulation and abstraction
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
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A nondeterministic weighted finite automaton (WFA) maps an input word to a numerical value. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. Many of these applications require the WFAs to be deterministic, or work substantially better when the WFAs are deterministic. Unlike NFAs, which can always be determinized, not all WFAs have an equivalent deterministic weighted automaton (DWFA). In Mohri (1997) [22], Mohri describes a determinization construction for a subclass of WFA. He also describes a property of WFAs (the twins property), such that all WFAs that satisfy the twins property are determinizable and the algorithm terminates on them. Unfortunately, many natural WFAs cannot be determinized. In this paper we study approximated determinization of WFAs. We describe an algorithm that, given a WFA A and an approximation factor t=1, constructs a DWFA A^' that t-determinizesA. Formally, for all words w@?@S^*, the value of w in A^' is at least its value in A and at most t times its value in A. Our construction involves two new ideas: attributing states in the subset construction by both upper and lower residues, and collapsing attributed subsets whose residues can be tightened. The larger the approximation factor is, the more attributed subsets we can collapse. Thus, t-determinization is helpful not only for WFAs that cannot be determinized, but also in cases determinization is possible but results in automata that are too big to handle. We also describe a property (the t-twins property) and use it in order to characterize t-determinizable WFAs. Finally, we describe a polynomial algorithm for deciding whether a given WFA has the t-twins property.