On the Shuffle Automaton Size for Words

We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v which ensure a quadratic upper bound on the state size of u shuffled with v. Moreover, switching only two letters within one of u or v is enough to trigger the change from quadratic to exponential

Non-Deterministic Finite Cover Automata

The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA ’98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language using a Non-deterministic Finite Automata (NFA) may significantly reduce the number of required states. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for non-deterministic finite cover automata (NFCA) and l-non-deterministic finite cover automaton (l-NFCA), we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs

Testing Identifiable Kernel P Systems Using an X-machine Approach

This paper presents a testing approach for kernel P systems (kP systems), based on the X-machine testing framework and the concept of cover automaton. The testing methodology ensures that the implementation conforms the speci cations, under certain conditions, such as the identi ably concept in the context of kernel P systems

Minimal cover-automata for finite languages

AbstractA cover-automaton A of a finite language L⊆Σ∗ is a finite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic finite cover automaton (DFCA) of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In this paper, we describe an efficient algorithm that, for a given DFA accepting a finite language, constructs a minimal deterministic finite cover-automaton of the language. We also give algorithms for the boolean operations on deterministic cover automata, i.e., on the finite languages they represent

Incomplete Transition Complexity of Basic Operations on Finite Languages

The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of boolean operations, concatenation, star, and reversal. For all operations we give tight upper bounds for both description measures. We correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right automaton is larger than the left one. For all binary operations the tightness is proved using family languages with a variable alphabet size. In general the operational complexities depend not only on the complexities of the operands but also on other refined measures.Comment: 13 page

A New Technique for Reachability of States in Concatenation Automata

We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the concatenation of two languages, and thus in establishing the state complexity of concatenation as an operation. Typically, ad-hoc induction arguments are used to show particular states are reachable in concatenation automata. We prove some results that seem to capture the essence of many of these induction arguments. Using these results, reachability proofs in concatenation automata can often be done more simply and without using induction directly.Comment: 23 pages, 1 table. Added missing affiliation/funding informatio

Pattern Matching in Link Streams: a Token-based Approach

International audienceLink streams model the dynamics of interactions in complex distributed systems as sequences of links (interactions) occurring at a given time. Detecting patterns in such sequences is crucial for many applications but it raises several challenges. In particular, there is no generic approach for the specification and detection of link stream patterns in a way similar to regular expressions and automata for text patterns. To address this, we propose a novel automata framework integrating both timed constraints and finite memory together with a recognition algorithm. The algorithm uses structures similar to tokens in high-level Petri nets and includes non-determinism and concurrency. We illustrate the use of our framework in real-world cases and evaluate its practical performances

Regular and Context-Free Pattern Languages over Small Alphabets

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and non-context-free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results

Patterns with Bounded Treewidth

We show that any parameter of patterns that is an upper bound for the treewidth of appropriate encodings of patterns as relational structures, if restricted to a constant, allows the membership problem for pattern languages to be solved in polynomial time. Furthermore, we identify a new such parameter, called the scope coincidence degree