Computer Science

To model real-world software systems, modelling paradigms should support a form of compositionality. In interface theory and model-based testing with inputs and outputs, conjunctive operators have been introduced: the behaviour allowed by composed specification s1 ∧ s2 is the behaviour allowed by both partial models s1 and s2. The models at hand are non-deterministic interface automata, but the interaction between non-determinism and conjunction is not yet well understood. On the other hand, in the theory of alternating automata, conjunction and non-determinism are core aspects. Alternating automata have not been considered in the context of inputs and outputs, making them less suitable for modelling software interfaces. In this paper, we combine the two modelling paradigms to define alternating interface automata (AIA). We equip these automata with an observational, trace-based semantics, and define testers, to establish correctness of black-box interfaces with respect to an AIA specification.

A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of equivalence checking for the verification of anonymity, we study the algorithmic comparison of two labelled MDPs, in particular, whether there exist strategies such that the MDPs become equivalent/inequivalent, both in terms of trace equivalence and in terms of probabilistic bisimilarity. We provide the first polynomial-time algorithms for computing memoryless strategies to make the two labelled MDPs inequivalent if such strategies exist. We also study the computational complexity of qualitative problems about making the total variation distance and the probabilistic bisimilarity distance less than one or equal to one.

Context-free grammars are not able to model cross-serial dependencies in natural languages. To overcome this issue, Seki et al. introduced a generalization called m -multiple context-free grammars ( m -MCFGs), which deal with m -tuples of strings. We show that m -MCFGs are capable of comparing the number of consecutive occurrences of at most 2m different letters. In particular, the language { a n 1 1 a n 2 2 … a n 2m+1 k ∣ n 1 ≥ n 2 ≥⋯≥ n 2m+1 ≥0} is (m+1) -multiple context-free, but not m -multiple context-free.

We study the language inclusion problem L 1 ⊆ L 2 where L 1 is regular or context-free. Our approach relies on abstract interpretation and checks whether an overapproximating abstraction of L 1 , obtained by overapproximating the Kleene iterates of its least fixpoint characterization, is included in L 2 . We show that a language inclusion problem is decidable whenever this overapproximating abstraction satisfies a completeness condition (i.e., its loss of precision causes no false alarm) and prevents infinite ascending chains (i.e., it guarantees termination of least fixpoint computations). This overapproximating abstraction of languages can be defined using quasiorder relations on words, where the abstraction gives the language of all the words "greater than or equal to" a given input word for that quasiorder. We put forward a range of such quasiorders that allow us to systematically design decision procedures for different language inclusion problems such as regular languages into regular languages or into trace sets of one-counter nets, and context-free languages into regular languages. In the case of inclusion between regular languages, some of the induced inclusion checking procedures correspond to well-known state-of-the-art algorithms like the so-called antichain algorithms. Finally, we provide an equivalent language inclusion checking algorithm based on a greatest fixpoint computation that relies on quotients of languages and, to the best of our knowledge, was not previously known.

We give a new characterization of primitive permutation groups tied to the notion of completely reachable automata. Also, we introduce sync-maximal permutation groups tied to the state complexity of the set of synchronizing words of certain associated automata and show that they are contained between the 2 -homogeneous and the primitive groups. Lastly, we define k -reachable groups in analogy with synchronizing groups and motivated by our characterization of primitive permutation groups. But the results show that a k -reachable permutation group of degree n with 6≤k≤n−6 is either the alternating or the symmetric group.

Register pushdown automata (RPDA) is an extension of classical pushdown automata to handle data values in a restricted way. RPDA attracts attention as a model of a query language for structured documents with data values. The membership and emptiness problems for RPDA are known to be EXPTIME-complete. This paper shows the membership problem becomes PSPACE-complete and NP-complete for nondecreasing and growing RPDA, respectively, while the emptiness problem remains EXPTIME-complete for these subclasses.

We investigate the fine-grained complexity of liveness verification for leader contributor systems. These consist of a designated leader thread and an arbitrary number of identical contributor threads communicating via a shared memory. The liveness verification problem asks whether there is an infinite computation of the system in which the leader reaches a final state infinitely often. Like its reachability counterpart, the problem is known to be NP-complete. Our results show that, even from a fine-grained point of view, the complexities differ only by a polynomial factor. Liveness verification decomposes into reachability and cycle detection. We present a fixed point iteration solving the latter in polynomial time. For reachability, we reconsider the two standard parameterizations. When parameterized by the number of states of the leader L and the size of the data domain D, we show an (L + D)^O(L + D)-time algorithm. It improves on a previous algorithm, thereby settling an open problem. When parameterized by the number of states of the contributor C, we reuse an O*(2^C)-time algorithm. We show how to connect both algorithms with the cycle detection to obtain algorithms for liveness verification. The running times of the composed algorithms match those of reachability, proving that the fine-grained lower bounds for liveness verification are met.

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena that complements the more traditional approaches, for instance those based on differential equations. A comprehensive list of decision problems about the dynamical behavior of reaction systems (such as cycles and fixed/periodic points, attractors, and reachability) is provided along with the corresponding computational complexity, which ranges from tractable problems to PSPACE-complete problems.

We present a construction for the composition of subsequential transducers (representing conditional probabilistic models) with subsequential failure transducers (representing probabilistic models). Under certain conditions, satisfied by the corresponding transduction devices, a more efficient construction is applicable that avoids the creation of unnecessary states. Furthermore, the weights of the resulting failure transducers can be efficiently redistributed via weight pushing in the ⟨ R + ,+,×,0,1⟩ and ⟨ R + ,max,×,0,1⟩ semirings.

It can be shown that each permutation group G⊑ S n can be embedded, in a well defined sense, in a connected graph with O(n+|G|) vertices. Some groups, however, require much fewer vertices. For instance, S n itself can be embedded in the n -clique K n , a connected graph with n vertices. In this work, we show that the minimum size of a context-free grammar generating a finite permutation group G⊑ S n can be upper bounded by three structural parameters of connected graphs embedding G : the number of vertices, the treewidth, and the maximum degree. More precisely, we show that any permutation group G⊑ S n that can be embedded into a connected graph with m vertices, treewidth k, and maximum degree Δ , can also be generated by a context-free grammar of size 2 O(kΔlogΔ) ⋅ m O(k) . By combining our upper bound with a connection between the extension complexity of a permutation group and the grammar complexity of a formal language, we also get that these permutation groups can be represented by polytopes of extension complexity 2 O(kΔlogΔ) ⋅ m O(k) . The above upper bounds can be used to provide trade-offs between the index of permutation groups, and the number of vertices, treewidth and maximum degree of connected graphs embedding these groups. In particular, by combining our main result with a celebrated 2 Ω(n) lower bound on the grammar complexity of the symmetric group S n we have that connected graphs of treewidth o(n/logn) and maximum degree o(n/logn) embedding subgroups of S n of index 2 cn for some small constant c must have n ω(1) vertices. This lower bound can be improved to exponential on graphs of treewidth n ε for ε<1 and maximum degree o(n/logn) .