[pl-seminar] POPL practice talk today at 12 in 3310

["Loris D'Antoni" <loris@xxxxxxxxxxx>]

I'll be giving a POPL practice talk today at 12 in 3310.

Sorry for the very late notice, but I will literally finish the slides in the next 2 hours.

Please try to come and ask me hard questions!

Monadic second-order logic on finite sequences, D'Antoni and Venaes
We extend the weak monadic second-order logic of one successor on finite strings (M2L-STR) to symbolic alphabets by allowing character predicates to range over decidable quantifier free theories instead of finite alphabets. We call this logic, which is able to describe sequences over complex and potentially infinite domains, symbolic M2L-STR (S-M2L-STR). We then present a decision procedure for S-M2L-STR based on a reduction to symbolic finite automata, a decidable extension of finite automata that allows transitions to carry predicates and can therefore model symbolic alphabets. The reduction constructs a symbolic automaton over an alphabet consisting of pairs of symbols where the first element of the pair is a symbol in the original formulaâs alphabet, while the second element is a bit-vector. To handle this modified alphabet we show that the Cartesian product of two decidable Boolean algebras (e.g., the formulaâs one and the bit-vectorâs one) also forms a decidable Boolean algebras. To make the decision procedure practical, we propose two efficient representations of the Cartesian product of two Boolean algebras, one based on algebraic decision diagrams and one on a variant of Shannon expansions. Finally, we implement our decision procedure and evaluate the performance of our implementation on a comprehensive set of formulas.

Cheers,

-Loris