Perturbed Timed Automata
نویسندگان
چکیده
We consider timed automata whose clocks are imperfect. For a given perturbation error 0 < ε < 1, the perturbed language of a timed automaton is obtained by letting its clocks change at a rate within the interval [1 ε, 1 + ε]. We show that the perturbed language of a timed automaton with a single clock can be captured by a deterministic timed automaton. This leads to a decision procedure for the language inclusion problem for systems modeled as products of 1-clock automata with imperfect clocks. We also prove that determinization and decidability of language inclusion are not possible for multi-clock automata, even with perturbation. Comments From the 8th International Workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/182 "!$# #&%('*),+.-0/"1324 5)6%" "798:-9# ;< =>8?-@-9# A51. 5B.CEDGFIHJ ?C4KL+.MN+3CI 5B.O P QSR?TVUXW9Y$Z[T]\_^a` bdceW9RfRfZg^:hiU j RfTVj k QSR?TVUXW9Y$Z[T]\&l; jnm?Wpo hiTrq5\$sfm?TIm:Teq:j hiW9Y$Rf` t QuRfTiUvW9Y$Z[T]\_^a`&brw;_hihiTiRf`XTiZuj&\xQuY$yfj Rfj&z;_{ |Lj&}~Lj Tio R rpp L X W p` RfZ[TVm?W9Yd\$Ti}W0m*j s:\$`X}j&\Nj |f` Z[W phi`"@5Zj&Y;$W Ti}~4W9Y[b6Wp9\0Xf` Y jno TVUXWpR~4W9Y[\$s?Y$yfj&\$Ti`XR W9Y[Y$` YS XL\$|?W>?@@59N$ ¢¡i£&¤5¥ ?£0¥"*`&b;`Xy:\Nj TiRfWpm¦y"^hiW9\[\$TiR?oaT]\$Z>9hV`"N5Z>N|Lj R?oXW j&\§jYNj&\$W T]\$|fTiR¦\$|fW TiR"\$W9Y$U j hG ̈]x©a"«9G¬0® W*Z[|f`0 ̄\$|fj&\S\$|?W ~4W9Y[\$s?Y$y4W0m¢hVj&RfoXsfj; o Wn` b9hV`"N0j&R;°y4Wu0j ~:\$s?Y$W0my"^j v@±@@2 3 ́¤f3 ́μ$3·¶x\$TV}Wpm j&s;?\$`X}j\$`XR.d ̧G|fTiZ hiW0j m?Z*\$` j¦m:WppTiZ[Ti`XR1~?Y$`"pW0m:s?Y$Wb ́`&Yn;\$|fWhVj R?oXsfj oXW°TiRfphis?z Z[Ti`XR ~?Y$`Xy?hiWp}ob ́`&Y; Zg^:Zg\$Wp}Z }`5m?WphiW0maj Z ~:Y$`5m?s?9\$Z ` b<9z®phi`"@°j s:\$`X}j\Nj T]\$| Ti}~4W9Y[b6Wp9\ phi`"N5Zp WSj&hVZ;[` ~?Y$`UvWu\$|fj&\Gm?W9\$W9Y$}TiR?TV»pj&\$Ti`XR j RLmm:WppTVmfj&yfTihiTi;\±^a` b hVj R?oXsfj oXW*TiRfphis?Z[TV` R(j&Y;$W Rf`&\S~4` Z[Z[TVy?hiW*b6` Yu} sfh]\$T]z®phi`"@°j s:\$`X}j\Nj:LW9UvWpR T]\$| ~4W9Y[\$s:Y$yLj\$TV` R3 1⁄4 1⁄2f3⁄4x¿4ÀIÁ§Â Ã*ÄÅ¿IÆ$Áx3⁄4 =-p :C4Ç,7@Ç68:B3 5)5 5+I7@8:È 579 §C48§BI8:7 :C4È¢Ç,7< 5Bn#&ÉLÊ.),Ç ́ËÇ,7È¢84C4#&)6Ç,B.̧85ÍL7@Ç6È¢#x 5B.CnË&8:B.M@# Îf+I# B?79),Ï Ð±ÑÒÓpÔ(Õ"Ö4Ð[×"ÒÕ"Ð[Õ¢Ø,ÙÚÛ #&-9# Ç6Bf7@-984C4+.Ë#XC :M§ °Í·8:-9È 5)rBI8:79 "79Ç,8?B(798¢È 84C4# )r7@K.#Ü3# K. v%LÇ,8?85Íu-9# :)VÝ_7@Ç6È¢# M@Ï4M$79#&ÈM Fe=>Ç6È¢# C 5+4798:È "7p ( :-@#°Þ.BIÇ,7@# 5+I7@8:È 579 #ÉL7@# B.C4# C
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