# Tagged Questions

A partial order is a binary relation over a set which is reflexive, antisymmetric, and transitive.

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### Two preorders with same glb

I have a set $S$ with two preorders $\mathord{\le}_1,\mathord{\le}_2\subseteq S\times S$ which a priori are unrelated. Let $\equiv_1$ and $\equiv_2$ be the induced equivalences (i.e., $x\equiv_1 y$ ...
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### Is it #P-hard to compute the number of antichains of a distributive lattice?

An antichain of a poset $(P, <)$ is a subset of pairwise incomparable elements, namely, a subset $A \subseteq P$ such that there are no $x, y \in A$ with $x < y$. By a result of Provan and Ball, ...
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### Determining what can be achieved by a permutation of elements of a noncommutative group

Fix a finite group $G$. I am interested in the following decision problem: the input is some elements of $G$ with a partial order on them, and the question is whether there is a permutation of the ...
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### Completeness of the quotient of the power set lattice of a partial order induced by the Hoare pre-order

Let $(P,\le)$ be a partially ordered set and $\preceq$ the Hoare pre-order on its subsets, i.e. for $X,Y\subseteq P$, $X\preceq Y$ iff $\forall x\in X:\exists y\in Y:x\le y$. Let $\sim$ be the ...
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### Reconstructing labeled poset from linear extensions

Let $(P, <, \mu)$ be a labeled poset, that is, a partial order $(P, <)$ with a labeling function $\mu$ that maps the elements of $P$ to labels in an alphabet $\Sigma$. A label list (or word) is ...
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### Complexity of counting poset automorphisms

A (finite) poset $P = (X, <)$, or partially ordered set, is a (finite) set $X$ equipped with a transitive antisymmetric relation $<$; it can be equivalently seen as a DAG $G = (X, E)$ that is ...
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### The rank-polynomial of a graded poset

Let $P$ be a graded poset with rank function $r$. We may then define its rank-polynomial as: $R_P(q) = \sum_{x \in P} q^{r(x)}$. This definition can be applied to several interesting posets, for ...
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### On finding a chain decomposition of a Partial Order

I am reading a paper by Daskalakis et al. entitled "Sorting and Selection in Posets". http://arxiv.org/abs/0707.1532 In that paper it is presented an enhancement to the algorithm Poset-...
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### My exact divide-conquer algorithm for counting antichain in a poset?

This post is a little lengthy, thank your for your patience for reading. ^_^ As known, counting antichains in a poset is #P-complete, so it is NP-hard to get the exact answer. Following is my simple ...
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### Is counting maximal cliques in an incomparability graph #P-complete?

This question is motivated by a MathOverflow question by Peng Zhang. Valiant showed that counting maximal cliques in a general graph is #P-complete, but what if we restrict to incomparability graphs (...
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### Lattice problems

There has been a fair amount of work on computational problems for partial orders (e.g., recognition, jump number, comparability graph recognition, etc...). I am curious what work specific to ...
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### reference for lexicographic path ordering

Can you recommend a good reference for reading about lexicographic/recursive path orderings? I'm currently reading about lpo's in Chapter 2 of the Handbook of Automated Reasoning, 'Resolution Theorem ...
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### Well Defined Ordering Relations in Object Oriented Type Systems [closed]

In any Object-Oriented type system the type relation of two objects A and B can be characterized in exactly one of the following ways: A has the same type as B A is a subtype of B B is a subtype of ...
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### Partially Ordered CFG

I'm looking for work about partially ordered context-free grammars. I've found one paper, which seems to simplify the problem too much (in addition to some technical mistakes, as far as I can tell). ...
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### Extension of a partial order to a total of partitions of a weak alternating automaton

My problem is this: given a weak alternating automaton and its partitions, and given a partial order on these partitions, how do we extend the partial order to a total order? The partitions of weak ...
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### The complexity of checking whether two DAG have the same number of topological sorts

This problem is highly related to the CNF one. Here is the problem: given two DAG (directed acyclic graphs), if they have the same counting of topological sorts, answer "Yes", otherwise, answer "No". ...