Incomplete operational transition complexity of regular languages

The state complexity of basic operations on regular languages considering complete deterministic finite automata (DFA) has been extensively studied in the literature. But, if incomplete DFAs are considered, transition complexity is also a significant measure. In this paper we study the incomplete (deterministic) state and transition complexity of some operations for regular and finite languages. For regular languages we give a new tight upper bound for the transition complexity of the union, which refutes the conjecture presented by Y. Gao et al. For finite languages, we correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right operand is larger than the left one. We also present some experimental results to test the behavior of those operations on the average case, and we conjecture that for many operations and in practical applications the worst-case complexity is seldom reached

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

Transition Complexity of Incomplete DFAs

In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained. It is shown that the transition complexity results for union and complementation are very different from the state complexity results for the same operations. However, for intersection, the transition complexity result is similar to that of state complexity.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Unrestricted State Complexity of Binary Operations on Regular and Ideal Languages

We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the state complexity of any binary boolean operation on $L'_m$ and $L_n$ is $mn$, and that of product (concatenation) is $m 2^n - 2^{n-1}$. In contrast to this, we show that if $L'_m$ and $L_n$ are over different alphabets, the state complexity of union and symmetric difference is $(m+1)(n+1)$, that of difference is $mn+m$, that of intersection is $mn$, and that of product is $m2^n+2^{n-1}$. We also study unrestricted complexity of binary operations in the classes of regular right, left, and two-sided ideals, and derive tight upper bounds. The bounds for product of the unrestricted cases (with the bounds for the restricted cases in parentheses) are as follows: right ideals $m+2^{n-2}+2^{n-1}$ ($m+2^{n-2}$); left ideals $mn+m+n$ ($m+n-1$); two-sided ideals $m+2n$ ($m+n-1$). The state complexities of boolean operations on all three types of ideals are the same as those of arbitrary regular languages, whereas that is not the case if the alphabets of the arguments are the same. Finally, we update the known results about most complex regular, right-ideal, left-ideal, and two-sided-ideal languages to include the unrestricted cases.Comment: 30 pages, 15 figures. This paper is a revised and expanded version of the DCFS 2016 conference paper, also posted previously as arXiv:1602.01387v3. The expanded version has appeared in J. Autom. Lang. Comb. 22 (1-3), 29-59, 2017, the issue of selected papers from DCFS 2016. This version corrects the proof of distinguishability of states in the difference operation on p. 12 in arXiv:1609.04439v

Alternating, private alternating, and quantum alternating realtime automata

We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we present two equivalent definitions of realtime private alternating finite automata (PAFAs). We show that the emptiness problem is undecidable for PAFAs. Furthermore, PAFAs can recognize some nonregular unary languages, including the unary squares language, which seems to be difficult even for some classical counter automata with two-way input. Regarding quantum finite automata (QFAs), we show that the emptiness problem is undecidable both for universal QFAs on general alphabets, and for alternating QFAs with two alternations on unary alphabets. On the other hand, the same problem is decidable for nondeterministic QFAs on general alphabets. We also show that the unary squares language is recognized by alternating QFAs with two alternations

Logic-Based Specification Languages for Intelligent Software Agents

The research field of Agent-Oriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research sub-field studies how formal methods can be used for AOSE. This paper presents a detailed survey of six logic-based executable agent specification languages that have been chosen for their potential to be integrated in our ARPEGGIO project, an open framework for specifying and prototyping a MAS. The six languages are ConGoLog, Agent-0, the IMPACT agent programming language, DyLog, Concurrent METATEM and Ehhf. For each executable language, the logic foundations are described and an example of use is shown. A comparison of the six languages and a survey of similar approaches complete the paper, together with considerations of the advantages of using logic-based languages in MAS modeling and prototyping.Comment: 67 pages, 1 table, 1 figure. Accepted for publication by the Journal "Theory and Practice of Logic Programming", volume 4, Maurice Bruynooghe Editor-in-Chie