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

Nondeterministic streaming string transducers

We introduce nondeterministic streaming string transducers (nssts) – a new computational model that can implement MSO-definable relations between strings. An nsst makes a single left-to-right pass on the input string and uses a finite set of string variables to compute the output. In each step, it reads one input symbol, and updates its string variables in parallel with a copyless assignment. We show that the expressive power of nsst coincides with that of nondeterministic MSO-definable transductions. Further, we identify the class of functional nsst; these allow nondeterministic transitions, but for every successful run on a given input generates the same output string. We show that deciding functionality of an arbitrary nsst is decidable with pspace complexity, while the equivalence problem for functional nsst is pspace-complete. We also show that checking if the set of outputs of an nsst is contained within the set of outputs of a finite number of dssts is decidable in pspace

On Weakly Ambiguous Finite Transducers

Abstract. By weakly ambiguous (finite) transducers we mean those transducers that, although being ambiguous, may be viewed to be at arm’s length from unambiguity. We define input-unambiguous (IU) and input-deterministic (ID) transducers, and transducers with finite codomain (FC). IU transductions are characterized by nondeterministic bimachines and ID transductions can be represented as a composition of sequential functions and finite substitutions. FC transductions are recognizable and can be expressed as finite unions of subsequential func-tions. We place these families along with uniformly ambiguous (UA) and finitely ambiguous (FA) transductions in a hierarchy of ambiguity. Fi-nally, we show that restricted nondeterministic bimachines characterize FA transductions. Perhaps the most important aspect of this work con-sists in defining nondeterministic bimachines and describing their power by linking them with weakly ambiguous finite transducers (IU and FA).

Safety Problems Are NP-complete for Flat Integer Programs with Octagonal Loops

Abstract. This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and, more generally, octagonal relations, labeling the transitions on the loops. The proof is based on the fact that the sequence of powers {Ri}∞i=1 of such relations can be encoded as a periodic sequence of matrices, and that both the prefix and the period of this sequence are 2O(||R||2) in the size of the binary encoding ||R||2 of a relation R. This result allows to characterize the complexity of the reachability problem for one of the most studied class of counter machines [8, 11], and has a potential impact on other problems in program verification.

Model Checking Recursive Programs with Numeric Data Types

Abstract. Pushdown systems (PDS) naturally model sequential recur-sive programs. Numeric data types also often arise in real-world pro-grams. We study the extension of PDS with unbounded counters, which naturally model numeric data types. Although this extension is Turing-powerful, reachability is known to be decidable when the number of rever-sals between incrementing and decrementing modes is bounded. In this paper, we (1) pinpoint the decidability/complexity of reachability and linear/branching time model checking over PDS with reversal-bounded counters (PCo), and (2) experimentally demonstrate the effectiveness of our approach in analysing software. We show reachability over PCo is NP-complete, while LTL is coNEXP-complete (coNP-complete for fixed formulas). In contrast, we prove that EF-logic over PCo is undecidable. Our NP upper bounds are by a direct poly-time reduction to satisfaction over existential Presburger formulas, allowing us to tap into highly opti-mized solvers like Z3. Although reversal-bounded analysis is incomplete for PDS with unbounded counters in general, our experiments suggest that some intricate bugs (e.g. from Linux device drivers) can be discov-ered with a small number of reversals. We also pinpoint the decidabil-ity/complexity of various extensions of PCo, e.g., with discrete clocks.