000			02775nam a2200265Ia 4500
008			160627s2013||||xx |||||||||||||| ||und||
080			_aHBNI Th64
100			_aSreejith, A.V. _eauthor
245			_aRegular quantifiers in Logics
260			_c2013
300			_a130p.
502			_a2013
502			_bPh.D
502			_cHBNI
520	3		_aIn this thesis, we study logic on words extended with regular quantifiers. Modulo counting quantifiers are one particular example of such quantifiers, which have been well studied in the past. These quantifiers can be generalized to group quantifiers and further to monoid quantifiers all being regular quantifiers. The logics we extend can be classified into two parts. In the first part, we look at logics which define regular languages like FO[<] and linear temporal logic (LTL). We extend these logics with the above mentioned regular quantifiers. In the second part, we look at regular quantifiers over a linear order and an addition function which respects the linear order. In the first part of our work, we show that LTL extended with modulo counting/ group operators (LTLgrp) and FO[<] extended with modulo counting/group quantifiers (FOgrp[<]), both accept the same set of languages. We then go on to show that the satisfiability and model checking for LTLgrp is PSPACE-complete. We also look at satisfiability of various fragments of this logic. Then we show that the two variable fragment of FOgrp[<] is EXPSPACE-complete. We also analyse certain important sublogics. In the second part of our work, we study first order logic with a linear order and the arithmetic predicate, +. We first show that the two variable fragment of FOmod[<,+] is undecidable. Then we show that over a unary alphabet satisfiability of FOmod[<,+] is 2EXPSPACE. Finally we investigate the expressive power of M[<,+], where M is a set of monoid quantifiers. We show, using the concept of a neutral letter [BIL+05], that the class of neutral letter languages definable in M[<,+] is equivalent to those definable in M[<]. Using the above claim, we are able to show that the logics M1[<,+] is different from M2[<,+], if the set of monoid quantifiers M1 and M2 are different. This lets us answer a conjecture of Roy and Straubing [RS07] that FO[<,+] and mod[<,+] are incomparable. We also show that given a regular language L, it is decidable whether L is definable in mod[<,+] or not.
650	1	4	_aComputer Science
653	1	0	_aFirst Order Logic
653	1	0	_aHBNI Th64
653	1	0	_aLinear Temporal Logic
653	1	0	_aLogics
720	1		_aKamal Lodaya _eThesis advisor [ths]
856			_uhttp://www.imsc.res.in/xmlui/handle/123456789/350
942			_2THESIS157 _cTHESIS
999			_c48862 _d48862