  Recent efforts in coding theory have focused on building codes for insertions
and deletions, called insdel codes, with optimal trade-offs between their
redundancy and their error-correction capabilities, as well as efficient
encoding and decoding algorithms.
  In many applications, polynomial running time may still be prohibitively
expensive, which has motivated the study of codes with super-efficient decoding
algorithms. These have led to the well-studied notions of Locally Decodable
Codes (LDCs) and Locally Correctable Codes (LCCs). Inspired by these notions,
Ostrovsky and Paskin-Cherniavsky (Information Theoretic Security, 2015)
generalized Hamming LDCs to insertions and deletions. To the best of our
knowledge, these are the only known results that study the analogues of Hamming
LDCs in channels performing insertions and deletions.
  Here we continue the study of insdel codes that admit local algorithms.
Specifically, we reprove the results of Ostrovsky and Paskin-Cherniavsky for
insdel LDCs using a different set of techniques. We also observe that the
techniques extend to constructions of LCCs. Specifically, we obtain insdel LDCs
and LCCs from their Hamming LDCs and LCCs analogues, respectively. The rate and
error-correction capability blow up only by a constant factor, while the query
complexity blows up by a poly log factor in the block length.
  Since insdel locally decodable/correctble codes are scarcely studied in the
literature, we believe our results and techniques may lead to further research.
In particular, we conjecture that constant-query insdel LDCs/LCCs do not exist.
