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  • 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., $\forall i ~.~ 0 \leq i &lt; n \rightarrow a[i+1]=a[i]-1$) 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\&quot;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 counter automata is shown to be<br>decidable as a consequence of earlier results on counter automata with a flat control structure
  • 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., $\forall i ~.~ 0 \leq i &lt; n \rightarrow a[i+1]=a[i]-1$) 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\&quot;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 counter automata is shown to be<br>decidable as a consequence of earlier results on counter automata with a flat control structure (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:PU76681!RIV10-MSM-26230___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA102/07/0322), Z(MSM0021630528)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 405691
http://linked.open...ai/riv/idVysledku
  • RIV/00216305:26230/08:PU76681
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • mathematical logic, arrays, decidability, decision procedure, formal verification, automata<br> (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [BB16B5692C95]
http://linked.open...v/mistoKonaniAkce
  • Budapešť
http://linked.open...i/riv/mistoVydani
  • Berlin
http://linked.open...i/riv/nazevZdroje
  • Foundations of Software Science and Computation Structures
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Vojnar, Tomáš
  • Habermehl, Peter
  • Radu, Iosif
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
http://purl.org/ne...btex#hasPublisher
  • Springer-Verlag
https://schema.org/isbn
  • 978-3-540-78497-5
http://localhost/t...ganizacniJednotka
  • 26230
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