A Boolean function is called vertex-transitive, if the partition of the Boolean cube into the preimage of 0 and the preimage of 1 is invariant under a vertex-transitive group of isometric transformations of the Boolean cube. Several constructions of vertex-transitive functions and some of their properties are presented.

Let $f$ be a Boolean function. Let $N(f)=\dnf(f)+\dnf(\neg f)$ be the
sum of the minimum number of monomials in a disjunctive normal form
for $f$ and $\neg f$. Let $p(f)$ be the minimum size of a partition
of the Boolean cube into disjoint subcubes such that $f$ is constant on
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Restricted branching programs are considered in complexity theory in
order to study the space complexity of sequential computations and
in applications as a data structure for Boolean functions. In this
paper (\oplus,k)-branching programs and (\vee,k)-branching
programs are considered, i.e., branching programs starting with a
... more >>>

Ordered binary decision diagrams (OBDDs) and their variants
are motivated by the need to represent Boolean functions
in applications. Research concerning these applications leads
also to problems and results interesting from theoretical
point of view. In this paper, methods from communication
complexity and ... more >>>

There are Boolean functions such that almost all orderings of
its variables yield an OBDD of polynomial size, but there are
also some exceptional orderings, for which the size is exponential.
We prove that for parity OBDDs the size for a random ordering
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Branching programs are a model for representing Boolean
functions. For general branching programs, the
satisfiability and nonequivalence tests are NP-complete.
For read-once branching programs, which can test each
variable at most once in each computation, the satisfiability
test is trivial and there is also a probabilistic polynomial
time test ... more >>>

For any Boolean function $f$ let $L(f)$ be its formula size
complexity in the basis $\{\land,\oplus,1\}$. For every $n$ and
every $k\le n/2$, we describe a probabilistic distribution
on formulas in the basis $\{\land,\oplus,1\}$ in some given set of
$n$ variables and of the ... more >>>

It is known that if a Boolean function f in n variables
has a DNF and a CNF of size at most N then f also has a
(deterministic) decision tree of size $\exp(O(\log n\log^2 N)$.
We show that this simulation {\em cannot} be ... more >>>

Branching programs (b.p.'s) or decision diagrams are a general
graph-based model of sequential computation. The b.p.'s of
polynomial size are a nonuniform counterpart of LOG. Lower bounds
for different kinds of restricted b.p.'s are intensively
investigated. An important restriction are so called $k$-b.p.'s,
where each computation reads each input ... more >>>

Branching programs (b.p.'s) or decision diagrams are a general
graph-based model of sequential computation. B.p.'s of polynomial
size are a nonuniform counterpart of LOG. Lower bounds for
different kinds of restricted b.p.'s are intensively investigated.
An important restriction are so called 1-b.p.'s, where each
computation reads each input bit at ... more >>>