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List of (unsolved) complexity problems arising from PL

What are some major, open computational complexity problems that arise from programming languages, especially program analysis and compilation? I am looking for problems on the lines of "the time complexity of Hindley-Milner type inference" or "the…
xrq
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Using Dependent Type Theory for Categories that are not LCCC

I have recently been working with polynomial functors and monads based mostly on Gambino-Kock. There they define polynomial functors in a Locally Cartesian Closed Category (LCCC) and extensively use dependent type theory to define constructions on…
Max New
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What is the complexity of this graph problem?

Given a simple undirected graph $G$, find a subset $A\neq \emptyset$ of vertices, such that for any vertex $x\in A$ at least half of the neighbors of $x$ are also in $A$, and the size of $A$ is minimum. That is, we are looking for a cluster, in…
Andras Farago
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Algorithms for set packing

There seems to be much work, for some NP-Hard problems, on developing fast exponential time exact algorithms (i.e., results of the form: Algorithm A solves problem $x$ in O(c^n) time, with c small). There seems to be a fair amount of work along…
Travis Service
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Example demonstrating the power of non-deterministic circuits

A non-deterministic Boolean circuit has, in addition to the ordinary inputs $x = (x_1,\dots,x_n)$, a set of "non-deterministic" inputs $y=(y_1,\dots,y_m)$. A non-deterministic circuit $C$ accepts input $x$ if there exists $y$ such that the circuit…
Gustav Nordh
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Intermediate problems between PSPACE and EXPTIME

Intermediate problems between P and NP are quite famous, and are sometimes considered as complexity classes by themselves. Do you know of any problem that is known to be PSPACE-hard and in EXPTIME, and resisting all efforts to be proved complete for…
Denis
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How not to compute the smallest circle enclosing a finite set of circles

Suppose we have a finite set $L$ of disks in $\mathbb{R}^2$, and we wish to compute the smallest disk $D$ for which $\bigcup L\subseteq D$. A standard way to do this is to use the algorithm of Matoušek, Sharir and Welzl [1] to find a basis $B$ of…
Robin Houston
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Is intersection of $k \ge 3$ graphic matroids in P?

It is known that intersection of three general matroids is NP-hard (source), which is done via reduction from Hamiltonian cycle. The reduction uses one graphic matroid and two connectivity matroids. A special case of a problem I am working on can be…
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Quadratic relationship between nondeterministic and deterministic space?

Savitch's theorem shows that $\mathrm{NSPACE}(f(n)) \subseteq \mathrm{DSPACE}(f(n)^2)$ for all large enough functions $f$, and proving that this is tight has been an open problem for decades. Suppose we approach the problem from the other end. For…
András Salamon
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How to cite Babai's new graph isomorphism result?

Recently, Babai has published a paper on STOC 2016 claiming that graph isomorphism can be solved in quasipolynomial time. In the beginning of 2017, Babai retracted the quasipolynomial claim due to some serious mistakes found by Harald Helfgott. As…
Nobo Dy
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A reference for a "more algebraic" approach to pushdown automata and CFLs?

In the Sakarovitch's book on automata theory, it is written in the introduction to the section on rationals in the free group that the material presented therein lays "the foundation of a truly mathematical theory of context-free languages".…
Jára Cimrman
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How can non-terminating $\lambda$-terms be turned into fixed-point combinators?

I've been thinking about these questions: Is there a typed lambda calculus which is consistent and Turing complete? https://cs.stackexchange.com/questions/65003/if-%CE%BB-x-x-x-has-a-type-then-is-the-type-system-inconsistent and there are already…
cody
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Is there a constant factor approximation algorithm for 2D rectangle coloring problem?

The problem we consider here is the extension of the well-known interval coloring problem. Instead of intervals we consider rectangles having sides parallel to axes. The objective is to color the rectangles using minimum number of colors such that…
Soumitra
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Formal Semantics of Programming Languages

I'm new to programming languages theory and I'm seeking for a good resource on a resource for formal semantics of programming languages. Specifically looking for structural operational semantics. I got some book recommendations. But I'm looking…
systemsfault
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How is Lambda Calculus a specific type of Term Writing system?

Church was associated with the Simply Typed Lambda Calculus. Indeed, it seems he explained the Simply Typed Lambda Calculus in order to reduce misunderstanding about the Lambda Calculus. When John McCarthy created Lisp - he based it on the Lambda…
hawkeye
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