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\relax
\citation{FWC:10:PPDP}
\citation{DR:14:AFDP,JLE:14:DPML,A:16:EPYU}
\citation{DMNS:06:CNSPD,D:06:DP}
\citation{DR:14:AFDP}
\citation{DR:14:AFDP,JLE:14:DPML}
\citation{M:12:SLSBDP,TKBW:17:PLAI}
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\@writefile{toc}{\contentsline {title}{Model Checking Differentially Private Properties}{1}}
\@writefile{toc}{\authcount {1}}
\@writefile{toc}{\contentsline {author}{Author}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\newlabel{section:introduction}{{1}{1}}
\citation{TKD:11:FVDPIS}
\citation{AACDP:15:OILDPM,GMP:16:PDPFPS}
\citation{WHRP:17:FADP,GHHNP:13:LDPDP,RP:10:DMTGS}
\citation{ZK:17:LTADPP}
\citation{BFGGHS:16:APCDP,BGGHS:16:PDPPC,BKOB:12:PRRDP,BDGKZ:13:VCDPASM,BGAHKS:14:PDPHL,BGAHRS:15:HOARRT,BFGAGHS:16:DPBP}
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\@writefile{toc}{\contentsline {section}{\numberline {2}Preliminaries}{2}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Markov Chains and Markov Decision Processes}{3}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Survey Mechanism}{4}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Truncated $\alpha $-Geometric Mechanism}{5}}
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\@writefile{toc}{\contentsline {section}{\numberline {4}The Logic $\textsf {dpCTL*}\xspace $}{7}}
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\@writefile{loa}{\contentsline {algorithm}{\numberline {2}{\ignorespaces SAT($K$, $\mathit {N}_{S}$, $\phi $)\relax }}{9}}
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\@writefile{toc}{\contentsline {section}{\numberline {6}Specifying Properties in $\textsf {dpCTL*}\xspace $}{10}}
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\@writefile{toc}{\contentsline {paragraph}{Differential Privacy.}{10}}
\@writefile{toc}{\contentsline {paragraph}{Compositionality.}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Markov Chain of Double Surveys\relax }}{11}}
\newlabel{figure:2-dp-mc}{{4}{11}}
\@writefile{toc}{\contentsline {paragraph}{Tighter Privacy Bounds for Composition.}{11}}
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\citation{DR:14:AFDP}
\citation{DR:14:AFDP}
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\@writefile{loa}{\contentsline {algorithm}{\numberline {3}{\ignorespaces Input: private database $d$, queries $f_i : d \rightarrow \{ 0, 1, \ldots , 5 \}$ with sensitivity $1$, threshold $t \in \{ 0, 1, \ldots , 5 \}$; Output: $a_1, a_2, \ldots $\relax }}{13}}
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\@writefile{toc}{\contentsline {paragraph}{Justification of query schedulers.}{15}}
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\newlabel{theorem:mdp-model-checking}{{1}{15}}
\citation{BK:08:PMC}
\citation{DR:14:AFDP}
\bibstyle{splncs03}
\bibdata{refs}
\bibcite{AACDP:15:OILDPM}{1}
\bibcite{BK:08:PMC}{2}
\bibcite{BaierKKKMW16}{3}
\bibcite{BDGKZ:13:VCDPASM}{4}
\bibcite{BFGAGHS:16:DPBP}{5}
\bibcite{BFGGHS:16:APCDP}{6}
\newlabel{proposition:sufficient-condition-mdp-model-checking}{{2}{16}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Conclusions}{16}}
\newlabel{section:conclusions}{{9}{16}}
\bibcite{BGAHKS:14:PDPHL}{7}
\bibcite{BGAHRS:15:HOARRT}{8}
\bibcite{BGGHS:16:PDPPC}{9}
\bibcite{BKOB:12:PRRDP}{10}
\bibcite{BiancoA95}{11}
\bibcite{ManneP92}{12}
\bibcite{CY95}{13}
\bibcite{CSS03}{14}
\bibcite{DMNS:06:CNSPD}{15}
\bibcite{DR:14:AFDP}{16}
\bibcite{D:06:DP}{17}
\bibcite{FWC:10:PPDP}{18}
\bibcite{GHHNP:13:LDPDP}{19}
\bibcite{GMP:16:PDPFPS}{20}
\bibcite{GRS:09:UUPM}{21}
\bibcite{GRS:12:UUPM}{22}
\bibcite{HanssonJ94}{23}
\bibcite{JLE:14:DPML}{24}
\bibcite{M:12:SLSBDP}{25}
\bibcite{Paz71}{26}
\bibcite{Put05}{27}
\bibcite{Rabin63}{28}
\bibcite{RP:10:DMTGS}{29}
\bibcite{TKBW:17:PLAI}{30}
\bibcite{TKD:11:FVDPIS}{31}
\bibcite{Tzeng92}{32}
\bibcite{WHRP:17:FADP}{33}
\bibcite{A:16:EPYU}{34}
\bibcite{ZK:17:LTADPP}{35}
\citation{Rabin63}
\citation{Paz71}
\@writefile{toc}{\contentsline {section}{\numberline {A}Proof of Theorem\nobreakspace {}1\hbox {}}{19}}
\@writefile{toc}{\contentsline {paragraph}{Emptiness problem:}{19}}