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Decidability of definability [article]

Manuel Bodirsky, Michael Pinsker, Todor Tsankov
2012 arXiv   pre-print
We also obtain decidability of the problem when we replace primitive positive definability by existential positive, or existential definability.  ...  We show decidability of this problem for all structures \Gamma\ that have a first-order definition in an ordered homogeneous structure \Delta\ with a finite relational signature whose age is a Ramsey class  ...  We will show here decidability of Expr pp (Γ) for a large class of structures Γ which we will now define. Let τ be a finite relational signature.  ... 
arXiv:1012.2381v4 fatcat:gfgrj2mcdzbbzhsrwtsq4am34m

Decidability of Definability

Manuel Bodirsky, Michael Pinsker, Todor Tsankov
2013 Journal of Symbolic Logic (JSL)  
We also obtain decidability of the problem when we replace primitive positive definability by existential positive, or existential definability.  ...  We show decidability of this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure Δ with a finite relational signature whose age is a Ramsey class and determined  ...  Theorem 1 then shows that primitive positive definability in fragments of Allen's Interval Algebra is decidable.  ... 
doi:10.2178/jsl.7804020 fatcat:la3j7odll5fyrnqripall56s5q

Decidability of Definability

Manuel Bodirsky, Michael Pinsker, Todor Tsankov
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
We also obtain decidability of the problem when we replace primitive positive definability by existential positive, or existential definability.  ...  We show decidability of this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure ∆ with a finite relational signature whose age is a Ramsey class and determined  ...  Theorem 1 then shows that primitive positive definability in fragments of Allen's Interval Algebra is decidable.  ... 
doi:10.1109/lics.2011.11 dblp:conf/lics/BodirskyPT11 fatcat:xob3ubxjqzd5tfaqdm7qukstze

Deciding FO-definability of regular languages [article]

Agi Kurucz, Vladislav Ryzhikov, Yury Savateev, Michael Zakharyaschev
2021 arXiv   pre-print
We prove that, similarly to known PSpace-completeness of recognising FO(<)-definability of the language L(A) of a DFA A, deciding both FO(<,C)- and FO(<,MOD)-definability are PSpace-complete.  ...  These FO-languages are known to define regular languages that are decidable in AC0 and ACC0, respectively.)  ...  Deciding L-definability of 2NFAs in PSpace Using the criterion Theorem 1 (i), Stern [25] showed that deciding whether the language of any given DFA is FO(<)-definable can be done in PSpace.  ... 
arXiv:2105.06202v5 fatcat:z6hsq4u2pbf4hkl36uo6rrueoi

Deciding the weak definability of Büchi definable tree languages

Thomas Colcombet, Denis Kuperberg, Christof Löding, Michael Vanden Boom, Marc Herbstritt
2013 Annual Conference for Computer Science Logic  
Cost automata can be used to help prove the decidability of some definability problems for regular languages of infinite trees.  ...  an acceptance game is just a labelling of the input tree with states (called a run) The weak definability problem is decidable if L(U) is deterministic.  ... 
doi:10.4230/lipics.csl.2013.215 dblp:conf/csl/ColcombetKLB13 fatcat:yr2d3x34wrcltgdxus2ftv6yai

Decidability of definability issues in the theory of real addition [article]

Alexis Bès, Christian Choffrut
2022 arXiv   pre-print
that the corresponding theory is decidable.  ...  In particular these results apply to the class of k-recognizable relations on reals, and allow us to prove that it is decidable whether a k-recognizable relation (of any arity) is l-recognizable for every  ...  More precisely we show that for every decidable expansion M of R, +, <, 1 such that every nonempty M-definable relation contains a point with rational components, one can decide whether or not a given  ... 
arXiv:2102.06160v4 fatcat:p7pzibnjg5bmxddhdobr2x3oq4

First Order Decidability and Definability of Integers in Infinite Algebraic Extensions of Rational Numbers [article]

Alexandra Shlapentokh
2014 arXiv   pre-print
We also obtain a structural sufficient condition for definability of the ring of integers over its field of fractions.  ...  We extend results of Videla and Fukuzaki to define algebraic integers in large classes of infinite algebraic extensions of Q and use these definitions for some of the fields to show the first-order undecidability  ...  Is the ring of integers of K inf first-order definable over K inf ? Question 1.2. Is the first-order theory of K inf decidable?  ... 
arXiv:1307.0743v3 fatcat:3r54m2fykff6bd73j7c3xpocga

Deciding Twig-definability of Node Selecting Tree Automata

Timos Antonopoulos, Dag Hovland, Wim Martens, Frank Neven
2015 Theory of Computing Systems  
Since the queries definable by NSTAs form a strict superset of twig-definable queries, we study the complexity of the problem to decide whether the query by a given NSTA is twig-definable.  ...  In addition, we show that it is also EXPTIME-complete to decide whether the query by a given NSTA is definable by a node selecting string automaton.  ...  First of all, it would be interesting to identify meaningful subclasses of NSTAs for which deciding twig-definability is tractable.  ... 
doi:10.1007/s00224-015-9623-7 fatcat:k547o5dygvagdpu5ivuehxwbwa

Deciding twig-definability of node selecting tree automata

Timos Antonopoulos, Dag Hovland, Wim Martens, Frank Neven
2012 Proceedings of the 15th International Conference on Database Theory - ICDT '12  
Since the queries definable by NSTAs form a strict superset of twig-definable queries, we study the complexity of the problem to decide whether the query by a given NSTA is twig-definable.  ...  In addition, we show that it is also EXPTIME-complete to decide whether the query by a given NSTA is definable by a node selecting string automaton.  ...  First of all, it would be interesting to identify meaningful subclasses of NSTAs for which deciding twig-definability is tractable.  ... 
doi:10.1145/2274576.2274584 dblp:conf/icdt/AntonopoulosHMN12 fatcat:yhnocxbynzatlpi7mqnqmzmxmm

Definability and decidability for rings of integers in totally imaginary fields [article]

Caleb Springer
2022 arXiv   pre-print
We show that the ring of integers of ℚ^tr is existentially definable in the ring of integers of ℚ^tr(i), where ℚ^tr denotes the field of all totally real numbers.  ...  This implies that the ring of integers of ℚ^tr(i) is undecidable and first-order non-definable in ℚ^tr(i).  ...  Undecidability The definability results in the preceding section have immediate consequences for decid- ability.  ... 
arXiv:2207.00140v1 fatcat:eu5bxn32end7pnyshma66pgueu

Characterizing and Deciding MSO-Definability of Macro Tree Transductions [chapter]

Joost Engelfriet, Sebastian Maneth
2000 Lecture Notes in Computer Science  
A macro tree transduction is MSO definable if and only if it is of linear size increase. Furthermore, it is decidable for a macro tree transduction whether or not it is MSO definable.  ...  Moreover we prove that it is decidable whether M 's transduction is of linear size increase, and hence whether it is MSO definable.  ...  In cases of decidability there is often a characterization of the subclass that is independent of the device that defines the whole class, analogous to our linear size increase characterization (as an  ... 
doi:10.1007/3-540-46541-3_45 fatcat:64las3bm35gqldwoda3tf7abdm

Definability and decidability of binary predicates for time granularity

Massimo Franceschet, Angelo Montanari, Adriano Peron, Guido Sciavicco
2006 Journal of Applied Logic  
In this paper we study the definability and decidability of binary predicates for time granularity in monadic languages interpreted over finitely and infinitely layered structures.  ...  We give a number of positive and negative results by reduction to/from a wide spectrum of decidable/undecidable problems.  ...  MPL P Decidable Decidable ? ? MCL P Decidable Decidable ? ? MSO = MSO P Decidable Decidable Undecidable Undecidable As we have already shown, ⊕ i 1 can be defined in terms of D i .  ... 
doi:10.1016/j.jal.2005.06.004 fatcat:fsofugplxrd6roh2aefmmgduki

Decidability and definability with circumscription

John S. Schlipf
1987 Annals of Pure and Applied Logic  
With general formula circumscription we can define several infinite cardinals, so the decidability problems are dependent upon the axioms of set theory.  ...  The set of structures definable (up to isomorphism) as first order definable subsets of countably infinite minimal models is the set of structures which are A2 ~ over the integers, for both forms of circumscription  ...  Also (L(to~k), e } Decidability and definability with circumscription 185 KP and (L(tro), ~) ~ KP.  ... 
doi:10.1016/0168-0072(87)90062-5 fatcat:kwayy4yrf5gcvhp5rch4yqoc4y

Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields [article]

Alexandra Shlapentokh
2006 arXiv   pre-print
We investigate Diophantine definability and decidability over some subrings of algebraic numbers contained in quadratic extensions of totally real algebraic extensions of Q.  ...  The definability and undecidability results for integral closures of "small" and "big" subrings of number fields in the infinite algebraic extensions of Q, previously shown by the author to hold for totally  ...  Given our assumptions on the degrees of the extensions, Gal(KE(β)/K) = Gal(K(β)/K))×Gal(E/Z). Let σ be the generator of Gal(K(β)/K) and let τ be a generator of Gal(E/Z).  ... 
arXiv:math/0606368v1 fatcat:fizhcnjkvvfy5oxkjs5fi2rxj4

MSO-definable Properties of Muller Context-Free Languages Are Decidable [chapter]

Zoltán Ésik, Szabolcs Iván
2016 Lecture Notes in Computer Science  
We show that it is decidable given an MSO-definable property P of countable words and a Muller context-free grammar G, whether every word in the language generated by G satisfies P .  ...  As a corollary, we obtain the main result of this note. Theorem 1. It is decidable for a given MCFL L and an MSO-definable property ϕ of words whether every member of L satisfies ϕ. Proof.  ...  Also, there is an algorithm to decide, for a Muller tree automaton and an MSO-definable property of trees whether every tree in the language L recognized by the automaton has property P .  ... 
doi:10.1007/978-3-319-41114-9_7 fatcat:4dumxlmqing7zhdfn62rwzd52e
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