Backtracking games and inflationary fixed points

Backtracking Games and Inflationary Fixed Points

We define a new class of games, called backtracking games. Backtracking games are essentially parity games with an additional rule allowing players, under certain conditions, to return to an earlier position in the play and revise a choice. This new feature makes backtracking games more powerful than parity games. As a consequence, winning strategies become more complex objects and computationa...

On Core XPath with Inflationary Fixed Points

In this report, we prove the undecidability of Core XPath 1.0 (CXP) [6] extended with an Inflationary Fixed Point (IFP) operator. We prove that the satisfiability problem of this language is undecidable. In fact, the fragment of CXP+IFP containing only the self and descendant axes is already undecidable.

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Games with 1-backtracking

We associate to any game G, in the sense of Set Theory, a variant of it we call bck(G). We show through examples that many relevant non-constructive proofs in Algebra and Combinatorics can be interpreted by recursive winning strategy over some game of the form bck(G). We further support this claim by proving that games of the form bck(G) are a sound and complete semantic for a sub-classical log...

Shallow Backtracking Points in an Intelligent Backtracking Schema