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43
MONA Implementation Secrets
, 2000
"... The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a p ..."
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Cited by 70 (6 self)
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The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a period of six years. Compared to the first naive version, the present tool is faster by several orders of magnitude. This speedup is obtained from many different contributions working on all levels of the compilation and execution of formulas. We present a selection of implementation "secrets" that have been discovered and tested over the years, including formula reductions, DAGification, guided tree automata, threevalued logic, eager minimization, BDDbased automata representations, and cacheconscious data structures. We describe these techniques and quantify their respective effects by experimenting with separate versions of the MONA tool that in turn omit each of them.
Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 68 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
Mona Fido: The LogicAutomaton Connection in Practice
, 1998
"... We discuss in this paper how connections, discovered almost forty years ago, between logics and automata can be used in practice. For such logics expressing regular sets, we have developed tools that allow efficient symbolic reasoning not attainable by theorem proving or symbolic model checking. ..."
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Cited by 53 (10 self)
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We discuss in this paper how connections, discovered almost forty years ago, between logics and automata can be used in practice. For such logics expressing regular sets, we have developed tools that allow efficient symbolic reasoning not attainable by theorem proving or symbolic model checking. We explain how the logicautomaton connection is already exploited in a limited way for the case of Quantified Boolean Logic, where Binary Decision Diagrams act as automata. Next, we indicate how BDD data structures and algorithms can be extended to yield a practical decision procedure for a more general logic, namely WS1S, the Weak Secondorder theory of One Successor. Finally, we mention applications of the automatonlogic connection to software engineering and program verification. 1
A Descriptive Approach to LanguageTheoretic Complexity
, 1996
"... Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly ContextFree Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and NonDefinability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT ..."
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Cited by 52 (3 self)
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Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly ContextFree Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and NonDefinability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT 2 / Contents Part II The Generative Capacity of GB Theories 59 7 Introduction to Part II 61 8 The Fundamental Structures of GB Theories 69 9 GB and Nondefinability in L 2 K;P 79 10 Formalizing XBar Theory 93 11 The Lexicon, Subcategorization, Thetatheory, and Case Theory 111 12 Binding and Control 119 13 Chains 131 14 Reconstruction 157 15 Limitations of the Interpretation 173 16 Conclusion of Part II 179 A Index of Definitions 183 Bibliography DRAFT 1<
Weighted automata and weighted logics
 In Automata, Languages and Programming – 32nd International Colloquium, ICALP 2005
, 2005
"... Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We g ..."
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Cited by 39 (7 self)
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Abstract. Weighted automata are used to describe quantitative properties in various areas such as probabilistic systems, image compression, speechtotext processing. The behaviour of such an automaton is a mapping, called a formal power series, assigning to each word a weight in some semiring. We generalize Büchi’s and Elgot’s fundamental theorems to this quantitative setting. We introduce a weighted version of MSO logic and prove that, for commutative semirings, the behaviours of weighted automata are precisely the formal power series definable with our weighted logic. We also consider weighted firstorder logic and show that aperiodic series coincide with the firstorder definable ones, if the semiring is locally finite, commutative and has some aperiodicity property. 1
MONA Version 1.4 User Manual
 Department of Computer Science, University of Aarhus
, 2001
"... Reproduction of all or part of this document is permitted on condition that it is unmodified, includes this copyright notice, and is distributed for free. The MONA tool is available under the GNU General Public License. ..."
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Cited by 32 (1 self)
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Reproduction of all or part of this document is permitted on condition that it is unmodified, includes this copyright notice, and is distributed for free. The MONA tool is available under the GNU General Public License.
Rex: Symbolic Regular Expression Explorer
 In ICST’10. IEEE
, 2010
"... Abstract—Constraints in form regular expressions over strings are ubiquitous. They occur often in programming languages like Perl and C#, in SQL in form of LIKE expressions, and in web applications. Providing support for regular expression constraints in program analysis and testing has several usef ..."
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Cited by 22 (11 self)
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Abstract—Constraints in form regular expressions over strings are ubiquitous. They occur often in programming languages like Perl and C#, in SQL in form of LIKE expressions, and in web applications. Providing support for regular expression constraints in program analysis and testing has several useful applications. We introduce a method and a tool called Rex, for symbolically expressing and analyzing regular expression constraints. Rex is implemented using the SMT solver Z3, and we provide experimental evaluation of Rex. Keywordsregular expressions; finite automata; satisfiability modulo theories; strings I.
The Monadic Quantifier Alternation Hierarchy over Graphs is Infinite
 In Twelfth Annual IEEE Symposium on Logic in Computer Science
, 1997
"... We show that in monadic secondorder logic over finite directed graphs, a strict hierarchy of expressiveness is obtained by increasing the (secondorder) quantifier alternation depth of formulas. Thus, the "monadic analogue" of the polynomial hierarchy is found to be strict, which solves a problem o ..."
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Cited by 21 (6 self)
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We show that in monadic secondorder logic over finite directed graphs, a strict hierarchy of expressiveness is obtained by increasing the (secondorder) quantifier alternation depth of formulas. Thus, the "monadic analogue" of the polynomial hierarchy is found to be strict, which solves a problem of Fagin. The proof is based on automata theoretic concepts (rather than EhrenfeuchtFrasse games) and starts from a restricted class of graphlike structures, namely finite twodimensional grids. We investigate monadic secondorder definable sets of grids where the width of grids is a function of the height. In this context, the infiniteness of the quantifier alternation hierarchy is witnessed by nfold exponential functions for increasing n. It is notable that these witness sets of the monadic hierarchy all belong to the complexity class NP, the first level of the polynomial hierarchy. 1 Introduction The subject of this paper is monadic secondorder logic over graphs. In this logic, one ca...
MSO definable string transductions and twoway finitestate transducers
 ACM Trans. Comput. Logic
, 2001
"... String transductions that are definable in monadic secondorder (mso) logic (without the use of parameters) are exactly those realized by deterministic twoway finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond ..."
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Cited by 19 (3 self)
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String transductions that are definable in monadic secondorder (mso) logic (without the use of parameters) are exactly those realized by deterministic twoway finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond to compositions of two nondeterministic twoway finite state transducers that have the finite visit property. Both families of mso definable string transductions are characterized in terms of Hennie machines, i.e., twoway finite state transducers with the finite visit property that are allowed to rewrite their input tape.
Syntactic Structures as Multidimensional Trees
"... We survey a sequence of results relating modeltheoretic and languagetheoretic
denability over an innite hierarchy of multidimensional treelike structures and explore
their applications to a corresponding range of theories of syntax. We discuss, in particular,
results for Government and Binding T ..."
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Cited by 14 (0 self)
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We survey a sequence of results relating modeltheoretic and languagetheoretic
denability over an innite hierarchy of multidimensional treelike structures and explore
their applications to a corresponding range of theories of syntax. We discuss, in particular,
results for Government and Binding Theory (GB), TreeAdjoining Grammar (TAG) and
Generalized PhraseStructure Grammar (GPSG) along with a generalized version of TAG
extending TAG in much the same way that GPSG extends CFLs. In addition, we look at a
hierarchy of language classes, Weir’s version of the Control Language Hierarchy, which is
characterized by denability in our hierarchy and speculate on possible linguistic signicance
of higher levels of these hierarchies.