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Existential second-order logic over strings

Thomas Eiter, Georg Gottlob, Yuri Gurevich
2000 Journal of the ACM  
Existential second-order logic (ESO) and monadic second-order logic (MSO) have attracted much interest in logic and computer science.  ...  Moreover, we determine the complexity of model checking over strings, for all ESO-pre x classes.  ...  Rosen for comments concerning decidability aspects of FO-pre x classes over nite strings they proposed Corollary 6.3 and suggested a reduction from domino problems for proving the undecidability p a r  ... 
doi:10.1145/331605.331609 fatcat:kebegomaljem5p7iwqzehhpsgm

Existential second-order logic over strings

T. Eiter, G. Gottlob, Y. Gurevich
Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)  
Existential second-order logic (ESO) and monadic second-order logic (MSO) have attracted much interest in logic and computer science.  ...  Moreover, we determine the complexity of model checking over strings, for all ESO-pre x classes.  ...  Rosen for comments concerning decidability aspects of FO-pre x classes over nite strings they proposed Corollary 6.3 and suggested a reduction from domino problems for proving the undecidability p a r  ... 
doi:10.1109/lics.1998.705640 dblp:conf/lics/EiterGG98 fatcat:nvh2jw26lfbmxksxcrpbqf2khu

Page 3011 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
logic over strings.  ...  The present paper is concerned with the expressive power on strings of fragments of existential second-order logic which are defined by restricting the form of the first-order matrix (called prefix fragments  ... 

On translations of temporal logic of actions into monadic second-order logic

A. Rabinovich
1998 Theoretical Computer Science  
We will show that 3rLA is not definable in monadic second-order logic over a discretetime structure.  ...  On the other hand, we will show that gTLA 'corresponds' to the standard second-order existential quantifier of monadic second-order logic in a continuous time structure.  ...  It is well known [9] that the monadic second-order logic of order (L; ) is undecidable over the structure of real numbers.  ... 
doi:10.1016/s0304-3975(97)00075-3 fatcat:eqhew27b5fa4zpqinibwzrfwvm

One quantifier will do in existential monadic second-order logic over pictures [chapter]

Oliver Matz
1998 Lecture Notes in Computer Science  
We show that every formula of the existential fragment of monadic second-order logic over picture models (i.e., nite, two-dimensional, coloured grids) is equivalent to one with only one existential monadic  ...  Every string language de nable in existential monadic second-order logic is a projection of a local string language. The above remark also holds if the word \existential" is removed.  ...  Introduction We study monadic second-order logic (MSO) over nite structures.  ... 
doi:10.1007/bfb0055826 fatcat:ngm4tgsx2ngotnlm6kngnh4tpu

Second-Order Logic over Strings: Regular and Non-regular Fragments [chapter]

Thomas Eiter, Georg Gottlob, Thomas Schwentick
2002 Lecture Notes in Computer Science  
We also give a brief survey of recent results on the complexity of evaluating existential second-order logic over graphs, and a list of interesting open problems.  ...  Recently, the regular and nonregular prefix classes of existential second-order logic (¦ ½ ½ ) were exhaustively determined.  ...  of monadic existential second-order logic.  ... 
doi:10.1007/3-540-46011-x_4 fatcat:wnrmwktrprhhnm4cuxl4zwwc2i

Logics for context-free languages [chapter]

Clemens Lautemann, Thomas Schwentick, Denis Thérien
1995 Lecture Notes in Computer Science  
predicate symbol, and the range of the second order quanti er is restricted to the class of matchings.  ...  More precisely, we show that the class of context{ free languages coincides with the class of those sets of strings which can be de ned by sentences of the form 9 b', where ' is rst order, b is a binary  ...  We therefore have to nd a logic whose expressive power lies between that of monadic second order logic on the one, and of rst order logic with one binary existential second order quanti er, on the other  ... 
doi:10.1007/bfb0022257 fatcat:yljkbhnfrzb23nn4hpewnugzui

Finite variability interpretation of monadic logic of order

A. Rabinovich
2002 Theoretical Computer Science  
We consider an interpretation of monadic second-order logic of order in the continuous time structure of ÿnitely variable signals.  ...  We provide a characterization of the expressive power of monadic logic.  ...  Completeness of the existential fragment of monadic logic An existential monadic formula is a formula of the form ∃X 1 : : : ∃X n : , where does not contain the second order quantiÿers.  ... 
doi:10.1016/s0304-3975(01)00126-8 fatcat:52btstv2nnh2bncukqdrl6bw6y

Descriptive Complexity, Lower Bounds and Linear Time [chapter]

Thomas Schwentick
1999 Lecture Notes in Computer Science  
This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order  ...  logic.  ...  Furthermore we wanted to point out that the logics that are used to characterize linear time complexity classes are not very di erent from several logics for which there have been non-expressibility proofs  ... 
doi:10.1007/10703163_2 fatcat:w2cssie5rrgftegs2hcsslajv4

Page 304 of Computational Linguistics Vol. 27, Issue 2 [page]

2001 Computational Linguistics  
Elgot that the sets of strings definable by existential sentences of monadic second-order logic (MSO) were exactly the regular languages; that is, a set of strings is regular if and only if it is a model  ...  existential sentence—that is, a sentence of the form 4X, ...4X,,{@|, where the X; are variables over properties or relations and © contains only first-order quantifiers.  ... 

Expressing versus Proving: Relating Forms of Complexity in Logic

A. Kolokolova
2010 Journal of Logic and Computation  
Complexity in logic comes in many forms.  ...  Lastly, we will touch upon the topic of formalizing complexity theory using logic, and the meta-question of complexity of logical reasoning about complexity-theoretic statements.  ...  Logics between first-order and existential second-order In the data complexity setting, first-order logic captures AC 0 and existential second-order logic already captures NP.  ... 
doi:10.1093/logcom/exq008 fatcat:lpla27ghunf5fmmvdanaoasaei

Expressive completeness of Temporal Logic of action [chapter]

Alexander Rabinovich
1998 Lecture Notes in Computer Science  
The paper compares the expressive power of monadic second order logic of order, a fundamental formalism in mathematical logic and theory of computation, with that of a fragment of Temporal Logic of Actions  ...  -strings and monadic second order logic (see 9, 8] for a survey).  ...  -string over .  ... 
doi:10.1007/bfb0055772 fatcat:ej6cu3byvndibmmcawt4myjfiy

A Theory of Restrictions for Logics and Automata [chapter]

Nils Klarlund
1999 Lecture Notes in Computer Science  
Unrestricted automata (recognizing unbounded strings of bit vectors) can be used to decide more expressive monadic second-order logics.  ...  We conclude that WS1S with first-order variables is the superior choice among monadic second-order logics.  ...  The string defines a set of positions from 0 to the length of the string minus 1; then, first-order variables range over this set, and second-order variables over its subsets.  ... 
doi:10.1007/3-540-48683-6_35 fatcat:llnt3ejb5bgfxfjek5hikwfrxa

0–1 laws by preservation

Thierry Lacoste
1997 Theoretical Computer Science  
We then investigate some fragments of the first-order infinitary logic L" and of second-order logic which are preserved under extension.  ...  This paper reveals new boundaries of O-1 laws for fragments of L" and of second-order logic.  ...  II;) of sentences beginning with a string of existential (resp. universal) second-order quantifiers, and followed by a first-order sentence.  ... 
doi:10.1016/s0304-3975(97)00086-8 fatcat:3u2f7vmchzgo5gvfx4ti63nprm

LINDSTRÖM QUANTIFIERS AND LEAF LANGUAGE DEFINABILITY

HANS-JÖRG BURTSCHICK, HERIBERT VOLLMER
1998 International Journal of Foundations of Computer Science  
We introduce second-order Lindström quantifiers and examine analogies to the concept of leaf language definability.  ...  The quantifier structure in a secondorder sentence defining a language and the quantifier structure in a first-order sentence characterizing the appropriate leaf language correspond to one another.  ...  We thank David Barrington for suggesting the examination of logically defined leaf languages as an interesting topic.  ... 
doi:10.1142/s0129054198000180 fatcat:ydfkliivj5gxtbr455rlzq7l2i
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