The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable

It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs

The Church Synthesis Problem with Parameters

For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of an operator Y=F(X) such that ψ(X,F(X)) is universally valid over Nat. B\"{u}chi and Landweber proved that the Church synthesis problem is decidable; moreover, they showed that if there is an operator F that solves the Church Synthesis Problem, then it can also be solved by an operator defined by a finite state automaton or equivalently by an MLO formula. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a unary predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of is decidable. We prove that the B\"{u}chi-Landweber theorem can be extended only to ultimately periodic parameters. However, the MLO-definability part of the B\"{u}chi-Landweber theorem holds for the parameterized version of the Church synthesis problem

Confluence of graph rewriting with interfaces

For terminating double-pushout (DPO) graph rewriting systems confluence is, in general, undecidable. We show that confluence is decidable for an extension of DPO rewriting to graphs with interfaces. This variant is important due to it being closely related to rewriting of string diagrams. We show that our result extends, under mild conditions, to decidability of confluence for terminating rewriting systems of string diagrams in symmetric monoidal categories

Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate

Introspective Pushdown Analysis of Higher-Order Programs

In the static analysis of functional programs, pushdown flow analysis and abstract garbage collection skirt just inside the boundaries of soundness and decidability. Alone, each method reduces analysis times and boosts precision by orders of magnitude. This work illuminates and conquers the theoretical challenges that stand in the way of combining the power of these techniques. The challenge in marrying these techniques is not subtle: computing the reachable control states of a pushdown system relies on limiting access during transition to the top of the stack; abstract garbage collection, on the other hand, needs full access to the entire stack to compute a root set, just as concrete collection does. \emph{Introspective} pushdown systems resolve this conflict. Introspective pushdown systems provide enough access to the stack to allow abstract garbage collection, but they remain restricted enough to compute control-state reachability, thereby enabling the sound and precise product of pushdown analysis and abstract garbage collection. Experiments reveal synergistic interplay between the techniques, and the fusion demonstrates "better-than-both-worlds" precision.Comment: Proceedings of the 17th ACM SIGPLAN International Conference on Functional Programming, 2012, AC