Promising Paths and Dead Ends in Evolutionary Theodicy

Traps, Invariants, and Dead-Ends

We consider the problem of deriving formulas that capture traps, invariants, and dead-ends in classical planning through polynomial forms of preprocessing. An invariant is a formula that is true in the initial state and in all reachable states. A trap is a conditional invariant: once a state is reached that makes the trap true, all the states that are reachable from it will satisfy the trap for...

Tendencies, Dead-ends, and Promising Ways. From Interface Ideas to New Programs

The mechanism of communication between users and devices is called interface. From time to time changes in interface significantly improve our work with computers even without any serious changes in programs themselves. Main ideas in PCs interface were introduced many years ago and since then there are no significant changes, while new devices show promising ways by using direct manipulation of...

Frobenius Problem and Dead Ends in Integers

Let a and b be positive, relatively prime integers. We show that the following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and b (it cannot be written as a non-negative or non-positive integer linear combination of a and b), and d is maximal (in the Cayley graph) with respect to this property. In...

African Development: Dead Ends and New Beginnings

Rainbow Paths with Prescribed Ends

It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if G is a connected graph distinct from C7, then there is a χ(G)-coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose colors are different. In [S. Akbari, V. Liaghat, and A. Nikzad. Colorful paths in vertex coloring of...