About: What else is decidable about integer arrays?

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.fit.vutbr.cz/~vojnar/Publications/hiv-arrays-tr-07.pdf
Description	This report is the full version of the corresponding FOSSCAS'08 paper, including full proofs of the achived results. In the work, we introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the $\exists^* \forall^$ first-order fragment and allows (1) Presburger constraints on existentially quantified variables, (2) difference constraints as well as periodicity constraints on universally quantified indices, and (3) difference constraints on values. In particular, using our logic, one can express constraints on consecutive elements of arrays (e.g., $\forall i ~.~ 0 \leq i < n \rightarrow a[i+1]=a[i]-1$) as well as periodic facts (e.g., $\forall i ~.~ i \equiv_2 0 \rightarrow a[i] = 0$). The decision procedure follows the automata-theoretic approach: we translate formulae into a special class of B\"uchi counter automata such that any model of a formula corresponds to an accepting run of an automaton, and vice versa. The emptiness problem for this class of This report is the full version of the corresponding FOSSCAS'08 paper, including full proofs of the achived results. In the work, we introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the $\exists^ \forall^*$ first-order fragment and allows (1) Presburger constraints on existentially quantified variables, (2) difference constraints as well as periodicity constraints on universally quantified indices, and (3) difference constraints on values. In particular, using our logic, one can express constraints on consecutive elements of arrays (e.g., $\forall i ~.~ 0 \leq i < n \rightarrow a[i+1]=a[i]-1$) as well as periodic facts (e.g., $\forall i ~.~ i \equiv_2 0 \rightarrow a[i] = 0$). The decision procedure follows the automata-theoretic approach: we translate formulae into a special class of B\"uchi counter automata such that any model of a formula corresponds to an accepting run of an automaton, and vice versa. The emptiness problem for this class of (en)
Title	What else is decidable about integer arrays? What else is decidable about integer arrays? (en)
skos:prefLabel	What else is decidable about integer arrays? What else is decidable about integer arrays? (en)
skos:notation	RIV/00216305:26230/08:PU78080!RIV10-MSM-26230___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA102/07/0322), Z(MSM0021630528)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Vojnar, Tomáš
http://linked.open.../riv/druhVysledku	A(V) - Audiovizuální tvorba se vzdáleným přístupem
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta informačních technologií
http://linked.open...dnocenehoVysledku	405690
http://linked.open...ai/riv/idVysledku	RIV/00216305:26230/08:PU78080
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	mathematical logic, arrays, decidability, decision procedure, formal verification, automata (en)
http://linked.open.../riv/klicoveSlovo	automata mathematical logic decidability arrays formal verification decision procedure
http://linked.open...i/riv/kodPristupu	V
http://linked.open...ontrolniKodProRIV	[94FB847E2221]
http://linked.open...in/vavai/riv/obor	JC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Advanced Formal Approaches in the Design and Verification of Computer-Based Systems
http://linked.open...UplatneniVysledku	2008
http://linked.open...iv/tvurceVysledku	Vojnar, Tomáš Habermehl, Peter Radu, Iosif
http://linked.open...n/vavai/riv/zamer	Výzkum informačních technologií z hlediska bezpečnosti
http://localhost/t...ganizacniJednotka	26230

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