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On the Determinization of Weighted Automata
 Journal of Automata, Languages and Combinatorics
, 2005
"... In the paper, we generalize an algorithm and some related results by Mohri [25] for determinization of weighted finite automata (WFA) over the tropical semiring. We present the underlying mathematical concepts of his algorithm in a precise way for arbitrary semirings. We define a class of semirings ..."
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In the paper, we generalize an algorithm and some related results by Mohri [25] for determinization of weighted finite automata (WFA) over the tropical semiring. We present the underlying mathematical concepts of his algorithm in a precise way for arbitrary semirings. We define a class of semirings in which we can show that the twins property is sufficient for the termination of the algorithm. We also introduce singlevalued WFA and give a partial correction of a claim by Mohri [25] by showing several characterizations of singlevalued WFA, e.g., the formal power series computed by a singlevalued WFA is subsequential iff it has bounded variation. Also, it is decidable in polynomial time whether a given WFA over the tropical semiring is singlevalued. 1
DECIDING UNAMBIGUITY AND SEQUENTIALITY OF POLYNOMIALLY AMBIGUOUS MINPLUS AUTOMATA
, 2009
"... This paper solves the unambiguity and the sequentiality problem for polynomially ambiguous minplus automata. This result is proved through a decidable algebraic characterization involving socalled metatransitions and an application of results from the structure theory of finite semigroups. It is n ..."
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This paper solves the unambiguity and the sequentiality problem for polynomially ambiguous minplus automata. This result is proved through a decidable algebraic characterization involving socalled metatransitions and an application of results from the structure theory of finite semigroups. It is noteworthy that the equivalence problem is known to be undecidable for polynomially ambiguous automata.
Strong Lexicalization of Tree Adjoining Grammars
"... Recently, it was shown (KUHLMANN, SATTA: Treeadjoining grammars are not closed under strong lexicalization. Comput. Linguist., 2012) that finitely ambiguous tree adjoining grammars cannot be transformed into a normal form (preserving the generated tree language), in which each production contains a ..."
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Recently, it was shown (KUHLMANN, SATTA: Treeadjoining grammars are not closed under strong lexicalization. Comput. Linguist., 2012) that finitely ambiguous tree adjoining grammars cannot be transformed into a normal form (preserving the generated tree language), in which each production contains a lexical symbol. A more powerful model, the simple contextfree tree grammar, admits such a normal form. It can be effectively constructed and the maximal rank of the nonterminals only increases by 1. Thus, simple contextfree tree grammars strongly lexicalize tree adjoining grammars and themselves. 1
Series which are both maxplus and minplus rational are unambiguous
 RAIRO  Theoretical Informatics and Applications 40
, 2006
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Finitevalued weighted automata
 In FSTTCS 2014
, 2014
"... Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is kvalued if the relation it defines has degree at most k, i.e., every set of values associated with ..."
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Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is kvalued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defined by kvalued automata, for all parameters k. We consider several measures to associate values with runs: sum, discountedsum, and more generally values in groups. We define a general procedure which decides, given a bound k and a WA over a group, whether this automaton is kvalued. We also show that any kvalued WA over a group, under some general conditions, can be decomposed as a union of k unambiguous WA. While inclusion and equivalence are undecidable problems for arbitrary sumautomata, we show, based on this decomposition, that they are decidable for kvalued sumautomata, and kvalued discounted sumautomata over inverted integer discount factors. We finally show that the quantitative Church problem is undecidable for kvalued sumautomata, even given as finite unions of deterministic sumautomata. 1
Quantitative monadic secondorder logic
 In Proceedings of LICS’13
, 2013
"... Abstract—While monadic secondorder logic is a prominent logic for specifying languages of finite words, it lacks the power to compute quantitative properties, e.g. to count. An automata model capable of computing such properties are weighted automata, but logics equivalent to these automata have o ..."
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Abstract—While monadic secondorder logic is a prominent logic for specifying languages of finite words, it lacks the power to compute quantitative properties, e.g. to count. An automata model capable of computing such properties are weighted automata, but logics equivalent to these automata have only recently emerged. We propose a new framework for adding quantitative properties to logics specifying Boolean properties of words. We use this to define Quantitative Monadic SecondOrder Logic (QMSO). In this way we obtain a simple logic which is equally expressive to weighted automata. We analyse its evaluation complexity, both data and combined complexity, and show completeness results for combined complexity. We further refine the analysis of this logic and obtain fragments that characterise exactly subclasses of weighted automata defined by the level of ambiguity allowed in the automata. In this way, we define a quantitative logic which has good decidability properties while being resonably expressive and enjoying a simple syntactical definition. I.
Residuation of tropical series: rationality issues
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3.2 An Example of a Polynomially Ambiguous WFA.................... 4
, 2008
"... We show that the termination of Mohri’s algorithm is decidable for polynomially ambiguous weighted finite automata over the tropical semiring which gives a partial answer to a question by Mohri [29]. The proof relies on an improvement of the notion of the twins property and a Burnside type character ..."
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We show that the termination of Mohri’s algorithm is decidable for polynomially ambiguous weighted finite automata over the tropical semiring which gives a partial answer to a question by Mohri [29]. The proof relies on an improvement of the notion of the twins property and a Burnside type characterization for the finiteness of the set of states produced by Mohri’s algorithm. ∗ An extended abstract was presented at Journées Montoises d’Informatique Théorique 2006.
Sequential? Sylvain Lombardy a, Jacques Sakarovitch b
"... This paper is a survey where we try to organise the known answers to the question whether a given finite automaton with multiplicity in a semiring K is equivalent to a sequential, or input deterministic, one. We shall see that depending on K, the question goes from obvious to open, that the answer g ..."
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This paper is a survey where we try to organise the known answers to the question whether a given finite automaton with multiplicity in a semiring K is equivalent to a sequential, or input deterministic, one. We shall see that depending on K, the question goes from obvious to open, that the answer goes from yes to undecidable. We review results on sequentiality in the cases of series of finite image, of series with multiplicity in fields, and of series with multiplicity in idempotent semirings.