4 research outputs found
Logics Meet 1-Clock Alternating Timed Automata
This paper investigates a decidable and highly expressive real time logic QkMSO which is obtained by extending MSO[<] with guarded quantification using block of less than k metric quantifiers. The resulting logic is shown to be expressively equivalent to 1-clock ATA where loops are without clock resets, as well as, RatMTL, a powerful extension of MTL[U_I] with regular expressions. We also establish 4-variable property for QkMSO and characterize the expressive power of its 2-variable fragment. Thus, the paper presents progress towards expressively complete logics for 1-clock ATA
Satisfiability Checking of Multi-Variable TPTL with Unilateral Intervals Is PSPACE-Complete
We investigate the decidability of the fragment of Timed
Propositional Temporal Logic (TPTL). We show that the satisfiability checking
of TPTL is PSPACE-complete. Moreover, even its 1-variable fragment
(1-TPTL) is strictly more expressive than Metric Interval Temporal
Logic (MITL) for which satisfiability checking is EXPSPACE complete. Hence, we
have a strictly more expressive logic with computationally easier
satisfiability checking. To the best of our knowledge, TPTL is the
first multi-variable fragment of TPTL for which satisfiability checking is
decidable without imposing any bounds/restrictions on the timed words (e.g.
bounded variability, bounded time, etc.). The membership in PSPACE is obtained
by a reduction to the emptiness checking problem for a new "non-punctual"
subclass of Alternating Timed Automata with multiple clocks called Unilateral
Very Weak Alternating Timed Automata (VWATA) which we prove to be
in PSPACE. We show this by constructing a simulation equivalent
non-deterministic timed automata whose number of clocks is polynomial in the
size of the given VWATA.Comment: Accepted in Concur 202
Generalizing Non-Punctuality for Timed Temporal Logic with Freeze Quantifiers
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are
prominent real-time extensions of Linear Temporal Logic (LTL). In general, the
satisfiability checking problem for these extensions is undecidable when both
the future U and the past S modalities are used. In a classical result, the
satisfiability checking for MITL[U,S], a non punctual fragment of MTL[U,S], is
shown to be decidable with EXPSPACE complete complexity. Given that this notion
of non punctuality does not recover decidability in the case of TPTL[U,S], we
propose a generalization of non punctuality called \emph{non adjacency} for
TPTL[U,S], and focus on its 1-variable fragment, 1-TPTL[U,S]. While non
adjacent 1-TPTL[U,S] appears to be be a very small fragment, it is strictly
more expressive than MITL. As our main result, we show that the satisfiability
checking problem for non adjacent 1-TPTL[U,S] is decidable with EXPSPACE
complete complexity