The tree width of an alternating finite automaton (AFA) measures the parallelism in all computations AFA on a given input. maximal existential (respectively, universal) A string w number choices parallel universal branches) one computation w. We give polynomial time algorithms deciding finiteness AFA’s and width. Also we algorithm that for with decides whether or not is finite. Finiteness decid...

2 Properties of Moduli Functors 22 2.1 Nilcomplete, Cohesive, and Integrable Functors . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Relativized Properties of Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Finiteness Conditions on Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4 Moduli of Spectral Deligne-Mumford St...

we prove that if $m$ is a monoid and $a$ a finite set with more than one element‎, ‎then the residual finiteness of $m$ is equivalent to that of the monoid consisting of all cellular automata over $m$ with alphabet $a$‎.

By imposing on the most general renormalizable quantum field theory the requirement of the absence of ultraviolet-divergent renormalizations of the physical parameters (masses and coupling constants) of the theory, finite quantum field theories in four space-time dimensions may be constructed. Famous “prototypes” of these form certain well-known classes of supersymmetric finite quantum field th...