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Prateek Karandikar

Publications and source records attributed to Prateek Karandikar.

8 recordsLinked to original sources
arXiv2019

The height of piecewise-testable languages and the complexity of the logic of subwords

The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been investigated in a systematic way. This article develops a series of new techniques for bounding the height of finite languages and of languages obtained by taking closures by subwords, superwords and related operations. As an application of these results, we show that $\mathsf{FO}^2(A^*,\sqsubseteq)$, the two-variable fragment of the first-order logic of sequences with the subword ordering, can only express piecewise-testable properties and has elementary complexity.

cs.LO↗
arXiv2019

The Ideal Approach to Computing Closed Subsets in Well-Quasi-Ordering

Elegant and general algorithms for handling upwards-closed and downwards-closed subsets of WQOs can be developed using the filter-based and ideal-based representation for these sets. These algorithms can be built in a generic or parameterized way, in parallel with the way complex WQOs are obtained by combining or modifying simpler WQOs.

cs.LO↗
arXiv2015

On the state complexity of closures and interiors of regular languages with subwords and superwords

The downward and upward closures of a regular language $L$ are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of $L$ are obtained dually by collecting words having all their subwords and superwords in $L$, respectively. We provide lower and upper bounds on the size of the smallest automata recognizing these closures and interiors. We also consider the computational complexity of decision problems for closures of regular languages.

cs.FL↗
arXiv2015

Decidability in the logic of subsequences and supersequences

We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the Σ_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO2 theory is decidable while the FO3 theory is undecidable.

cs.LO↗
arXiv2015

On Reachability for Unidirectional Channel Systems Extended with Regular Tests

"Unidirectional channel systems" (Chambart & Schnoebelen, CONCUR 2008) are finite-state systems where one-way communication from a Sender to a Receiver goes via one reliable and one unreliable unbounded fifo channel. While reachability is decidable for these systems, equipping them with the possibility of testing regular properties on the contents of channels makes it undecidable. Decidability is preserved when only emptiness and nonemptiness tests are considered: the proof relies on an elaborate reduction to a generalized version of Post's Embedding Problem.

cs.LO↗
arXiv2014

Generalized Post Embedding Problems

The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to undecidability.

cs.LO↗
arXiv2012

The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.

cs.LO↗