# Logics Meet 2-Way 1-Clock Alternating Timed Automata

@article{Krishna2021LogicsM2, title={Logics Meet 2-Way 1-Clock Alternating Timed Automata}, author={Shankara Narayanan Krishna and Khushraj Madnani and M. Mazo and Paritosh K. Pandya}, journal={ArXiv}, year={2021}, volume={abs/2107.12986} }

In this paper, we study the extension of 1-clock Alternating Timed Automata (1-ATA) with ability to read in both forward and backward direction, the 2-Way 1-clock Alternating Timed Automata (2-Way 1-ATA). We show that subclass of 2-Way 1-ATA with reset free loops (2-Way 1-ATA-rfl) is expressively equivalent to MSO[<] extended with Guarded Metric Quantifiers (GQMSO). Emptiness Checking problem for 2-Way 1-ATA-rfl (and hence GQMSO) is undecidable, in general. We propose a “non punctuality” like… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES

Generalizing Non-Punctuality for Timed Temporal Logic with Freeze Quantifiers

- Computer Science
- ArXiv
- 2021

This work proposes a generalization of non punctuality called non adjacency for TPTL[U,S], and shows that the satisfiability checking problem for non adjacent 1-TPTL[ U,S] is decidable with EXPSPACE complete complexity. Expand

On Decidable Extensions of Metric Temporal Logic

- PhD thesis, Indian Institute of Technology
- 2019

Revisiting timed logics with automata modalities

- Computer Science, Mathematics
- HSCC
- 2019

This paper shows that the logics EMITL0, ∞ (adding non-deterministic finite automata modalities into the fragment of MITL with only lower- and upper-bound constraints) and EECL (adding automatamodalities into ECL) are already as expressive as EMIT l, whereas the satisfiability and model-checking problems for EMITl are PSPACE-complete. Expand

Logics Meet 1-Clock Alternating Timed Automata

- Computer Science
- CONCUR
- 2018

The resulting logic QkMSO 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[ UI ] with regular expressions. Expand

The Compound Interest in Relaxing Punctuality

- Computer Science
- FM
- 2018

By providing a clean, automaton-based formal framework for non-punctual languages, MIRE is able to recover and extend several results in timed systems, and it is obtained that MIRE are expressively complete relative to a class of one-clock timed automata, which can be determinized using additional clocks. Expand

Making Metric Temporal Logic Rational

- Mathematics, Computer Science
- MFCS
- 2017

It is shown that $\regmtl$ has decidable satisfiability by giving an equisatisfiable reduction to $\mtl$, and a tight automaton-logic connection between $\sfmtl $ and partially ordered 1-clock alternating timed automata is shown. Expand

Transforming Two-Way Alternating Finite Automata to One-Way Nondeterministic Automata

- Mathematics, Computer Science
- MFCS
- 2014

It is proved that a two-way alternating infinite automaton with n states can be transformed to an equivalent one-way nondeterministic finite automaton (1NFA) with f(n) = 2Θ(n logn) states, and it is shown that complementing a 2AFA requires at least Ω( n logn] states. Expand

When is Metric Temporal Logic Expressively Complete?

- Mathematics, Computer Science
- CSL
- 2013

It is shown that full first-order expressiveness can be recovered with the addition of counting modalities, strongly supporting the assertion of Hirshfeld and Rabinovich that Q2MLO is one of the most expressive decidable fragments of FO(<,+1). Expand

Universality Analysis for One-Clock Timed Automata

- Computer Science
- Fundam. Informaticae
- 2008

This paper shows that if e-transitions or non-singular postconditions are allowed, then the one-clock universality problem is undecidable over both finite and infinite words, and presents a zone-based algorithm for solving the universalityproblem for single-clock timed automata. Expand

An Expressive Temporal Logic for Real Time

- Mathematics, Computer Science
- MFCS
- 2006

It is proved that all the modalities that can be expressed in a strong natural decidable predicate logic framework, are expressible in this temporal logic. Expand